Did you ever wonder what God thinks about you? Well, stay tuned on today's Move Your Mountain. You're going to find out exactly how God feels about you. We're also going to have some inspiring music. We're going to take Holy Communion together, and then we're going to pray over all of your prayer requests so you don't want to miss today's program. What all our sins and griefs to beg, to God in prayer. Oh, welcome everyone. And thank you so much for joining us today. I believe you are in for just an inspiring time as we get into the Lord's presence today. I'm Pastor Gary here with Pastor Myra, Pastor John and Pastor Rebecca. And it is great to be together, isn't it? It is, and we are so glad that you are here with us today. We are looking forward to what God is going to do amongst us, how he's going to move. I love, there's always an unexpected, because we're not prescript. We don't know what we're going to talk about here, but we do know that the Holy Spirit is here. And when he's here, some great things will happen. So get prepared today. Yes, yes, yes. And you know, if I'm not mistaken, it's two or three are gathered. We've exceeded that. We've got four. We've got four today.  And so I just can't wait. Yeah, expect God to do it today in your life. Expect him to move on your behalf because of his spirit, his presence among us. I'm excited about that. Well, remember, we do have prayer partners available. They are waiting to pray for you<PHONE_NUMBER>. If anything is on your heart, or if there's anything we're going to discuss today, call that number. Someone will agree with you in prayer. And then remember, get your communion elements, a cracker, a piece of bread, some juice in a cup so that when we partake together at the Lord's table, you can join in. You don't want to miss that. Well, one of my favorite Psalms, I love this Psalm, Psalm 16, starting there in verse one says, Preserve me, O God, for in you I put my trust.  And as for the saints who are on the earth, they are the excellent ones in whom is all my delight. Now, I have a pretty strong feeling there's a lot of Christians that don't know that God delights in us as Christians that he thinks about us the way that verse describes it. And I just want to say to you today, if you've got some wrong images, some false images, we were talking about how sometimes we get our image of our heavenly Father from our earthly Father, or from how other people have treated us. But I want you to know you need to see yourself like the Lord sees you. And number one, the first point you need to get this, the Lord, he delights in you. I think, Pastor Gary, that a lot of times we as believers, because we don't esteem ourselves like we should, and we should because even Jesus said in Matthew 22, he said, love your neighbor how as you do yourself. That's good. That's good. As you do yourself. So we have to change our perspective. We have to change how we look at God, how we look at ourselves, how we look at other believers. I thought about an old poem. It said, to live above with saints we love, oh, it will be glory. To live below with saints we know, it's quite a different story. But if we delight in, as God delights in us, we delight in one another understanding. We delight in you. You're watching today. We delight in you that we are in this together and God has put worth on us. He gave his only begotten Son, putting worth on us, delight in the Lord. He delights in you. We have a good life. Yeah, amen. And I think that's something that a lot of times I encounter a lot of people who have a faulty framework of who God is, not just from the perspective of, I love how you said that, Pastor Gary, because a lot of people we do see God through the lens of our earthly father or our earthly circumstances. But I also noticed people too that think, well, God didn't do this for me or God let me down here. And I love how you brought up, Pastor Myra, the fact that he has already paid the highest price for you that could be paid. I remember a young man who attends our church, came up to me one day and he had grown up in Christianity.  And he came up to me afterward and he said, I'd never heard it put that way and that just struck me so much. Because here's the thing, when you understand the inherent value in a thing, you will treat it in a way, commeserate with that inherent value. And so if someone was to give you a Rolls Royce or a Lamborghini, you would never take that off-roading in the woods or driving it through rivers and mud pals and smashing it through all the potholes here in the city of Pittsburgh, if you live here where we live. And in the same way, we do that with our own lives. We don't understand the inherent value of the price that is paid for us through Jesus Christ. And so we take and we allow certain things to happen to us or we even run ourselves through the muck of sin and just living below the standard that we are called to as saints of God. And that's why we need to be reminded. God delights in you. His delight is in you. You make the Father smile. And some of you might be saying, well, how can I make the Father smile? Look at the sin in my life. Look at all the areas where I failed Him. Do you understand that Jesus took all of your failures, all of your sins, all of your deficiencies and allowed them to be nailed with Him to the cross so that His Father's delight could arise in you? And Pastor Rebecca, I think it's high time for people all across this land, especially believers, those who are saints, but those who have not yet come to God to realize that the Father's delight is in them because of what the Son has done on our behalf.  And I think that as Christians, as believers, if we would begin to see that and visualize that and understand that what value we have in us, we wouldn't make some of the decisions that we've made. We wouldn't continue to make some of the bad choices that we make because we would see that God loves us so much. He gave us everything. So we should do that same thing and give Him everything that we have, everything that we desire, all our dreams, all our ambitions. We should line it up to God. What do you want from me? You gave me everything. So the least that I could do is give you my life. And as we do that as Christians, as we do that as God's children, He does take delight in us because He's saying, wow, you are actually following me. You're doing what I desire you to do. And when we do that, He blesses us when we have that walk of faith, when we walk in the ways that God wants us to, He doesn't have any other option but to bless us because He desires that. He loves to bless His kids. You know, I even think about the very one who was writing the Psalms. You know, when you think of David and all the things that he had gone through in his life, if anybody should stand there and say, God, I don't deserve this. I don't know why you would ever love me. And he probably did feel that way. But he also recognized who God was. He was his protector.  He saved him from every enemy that would come in his direction.  So if you are struggling with something right now, you give it over to God. Say, Lord, you see where the position that I am in right now and you know I don't want to be here. You know I want to be where you want me to be. Help me to follow you. Help me to make the right moves to follow you in the way that I should so that you can once again take delight in me so that I can make you proud. That's what we should all desire as his children to make him proud. We all know that scripture, delight yourself in the Lord. He'll grant you the desires of your heart. But this says the Lord delights himself in you. Think about that. He delights not because you've earned it, not because you deserve it, not because you've done anything. He just loves spending time with you. It's like a father who just loves when his children come. They're not asking for anything. They don't need anything. They just want to hang with their daddy. And you have a heavenly father who says you are his excellent one. Think about that. You're his excellent one.  And you are his excellent one because even when those failures do come up, he's not looking at you. He's looking at Jesus. He is looking at his beloved son. And Romans 832, one of my favorite verses of scripture says, and if he did not withhold Jesus from us, how will he not also along with Jesus? He already gave us his best, but he will also give us graciously all things.  Let it just blow all of those ideas of failure, all of those ideas of lack, all of those ideas of I'm not enough or I don't have enough. Look, you already have. If you have Jesus Christ, you have everything you need because the Father's delight is in Jesus and Jesus is in you. And so I just encourage you, let that resonate in your soul today. And maybe even if you got to jump up and skip around and have a little praise bake, because you know what, that's some good truth. Yes it is. And I like what you said. We love our neighbors only as much as we love ourselves. And I think we, people have a hard time loving souls, loving the lost, loving the broken, the hurting, because they don't like themselves. Absolutely, absolutely. And I think about as we were talking, or as you were saying a little bit earlier, a lot of times we will funnel our love, the love God has for us through our earthly fathers. And there's somebody watching right now. You didn't have a great father who loved you just right. And so you have problems letting God love you. And today God wants to heal you. Come on. He wants you to forgive your father, but also allow God to heal the hurt. They're not one in the same. Forgive them. He owes you nothing.   It says, I have set the Lord always before me. That's a great goal, isn't it? Because he is at my right hand. I shall not be moved. There are so many times when I hold my right hand up as close to me as I can. And I say, Lord, that's how close you are to me. He's my paracletos, the one who comes alongside of me.  You are never, ever, ever alone or by yourself. And point number two, that's it. He's as close to you as your right hand. Pastor Gray, this is why the Holy Spirit is so important to us. You know, when you say he's as close to us, he's our helper, he's our strength, he's that one that we need. Whenever you call on Jesus, the Holy Spirit is there with you. If you've accepted Christ, it says you've got that Holy Spirit. But the power of the Holy Spirit is in you and you can, you know that no matter what you are facing, that his peace will rule your heart. His strength, he'll give you the strength. When you feel weak in yourself, he says my grace is sufficient. My strength is made perfect in your weakness. So no matter what you are facing, you may feel like God is far away. But this verse says he is close, he is close to us. We just have to see him. We just have to recognize that he is there. And so many times we look at everything else going on in our lives that we push the vision of God out of our way and we don't see that he is there in the midst of the circumstance. He is just as much there in your bad times, in the valleys as he is in the good times, on the mountaintops. He is just as much there in darkness as he is in light, as he is in death, as he is in life. He is there with us at all times. So no matter what you are facing today at this very moment, he is with you. He sees it. He knows it. You are not alone. He sees everything you are facing, every decision that you have to make, every decision that maybe your family member has to make that is difficult for them. He sees the trials that they're going through and all you got to do is call on him and he's right there to answer you. That's awesome to know that we have a God who is not far off but he is right beside us every second of every day. And I think as you put your hand up, that right hand, I think about how close God is to us. He is the God of hope. There are those of you who right now you've been feeling hopeless in your situations and in your circumstances. Those things that you can't change but the God of hope is at your right hand and it says that the God of hope will cause hope to abound in you and we know that faith is the substance of what we hope for. Let God stir hope in you today. Let him because he's at your right hand waiting for you to just acknowledge him. He will do it for you. And you know that the crazy thing is even if you're God further away from you, your right hand goes with you wherever you go and so even if you extend your right hand as far away from you as possible, it just goes to show you God is never further than an arms distance away and I honestly believe because some of you are watching right now and you figure if God's with me why are all of these things just coming at me right now. I want you to think about this in a natural. If you're sitting there whether you're at home or in the nursing home, you're in the hospital, you're in prison, you're watching this on a mobile device in your car at a bus stop wherever you're watching this right now. If something flew at you out of the blue without even thinking you're going to throw your hands up to protect you. Sometimes God will allow things to come at you because he wants to see you how involuntarily it is for him to come up and block that thing from getting to you and so remember that and you're thinking about your right hand you're thinking about how near God is to you. You may think he's far away but he's never more than an arms distance but he is always ready to jump up and protect you to jump up and guard you and give you the strength that you need. That's one of the significant things in the scripture about the right hand and it is the position of strength. God is seated at a position of strength in your life. That's why David was able to say I will not be moved so whatever you're facing whatever's coming at you know that God is at your right hand and continue to keep the Lord always and in all ways before you because he will protect you from whatever's coming your way. There's someone watching you were abandoned by your natural father and because of that you are really struggling believing that God is that near to you that God loves you and delights in you and I just want you to call that prayer partner because I believe as Pastor Myra said there's a deep healing that God has to do in your life going all the way back to your childhood just breaking off of you generational curses we break that spirit of abandonment off of you today and I just want you to just hold up your right hand for a moment and just say quote that scripture Lord you are as close to me as my right hand and he is he loves you he delights in you you are his excellent one and he wants to set you for you've been believing lies from the enemy for years now and today is a day of freedom and deliverance turn around for you let's look at the last verse in chapter 16 it says you will show me the path of life and in your presence there is fullness of joy at your right hand there are pleasures forevermore and I just want to encourage you number three and finally stay in his presence in his presence it makes such a difference when you get into that atmosphere there have been so many times when I've been struggling with things in my own life personally and I've tried to deal with it on my own but that moment that I just say okay God I've got to bring you into this situation in this place we can say God I don't want you involved and we try to do it on our own and we can invite him but whenever I've invited him in those moments man that burden just lifts his peace comes in and we experience the pleasures that are at his right hand forevermore I want to encourage you today if that is where you are saying okay I'm struggling with this thing invite Christ in invite the Holy Spirit to come and make a difference in your life because he will and stay there stay in his presence once you experience God once you experience being in his presence there is nothing like it and you're going to want to keep going back and getting more and getting more it's kind of it's better than an addiction it is I hate using those carnal words but it's better than that because man when you get the fullness of Christ in you when you get his Holy Spirit working in your life you know that no matter what you are facing no matter what discouragement tries to come you have that shield of faith that rises up because you were a believer and you have on the armor of God that says it doesn't matter what comes my direction I know the God that I serve and I know that his presence is with me and I know that as I stay here and as I commune with him as I have that relationship with him what was it Moses said you know I don't want to go anywhere unless your presence goes with me Lord that's where I want to be in my life God I don't want to go anywhere and I pray that's your prayer today God I don't want to make another step I don't want to make another move without your presence we live in a world that we need the presence of Jesus we need the power of the Holy Spirit leading and directing our lives because if we don't have it we are going to feel hopeless like you said Pastor Myra we're going to feel hopeless so we need to stay in his presence immersed in his presence at all times I was thinking about that same chapter as you were reading that passage I thought about how God told Moses there's a place by me and I will hide you there in the cleft of the rock and I think about in the secret place of the most high God if we just abide there there's nothing like it as you were saying God wants you to live there with him in his presence fullness of joy not happiness based on the things that happen around us but that state of joy God wants you to be in his presence because their fullness of joy there's no greater joy than in his presence Amen and you know there's a reality that you can be in his presence and your circumstances keep you from keep you from being aware that you're in his presence I think of Cleopas and his friend right after the resurrection of Jesus they're on their way back out of town and Jesus pulls up next to them they're walking of course and here they are walking talking in the presence of the resurrected Lord himself but because their eyes had been so blinded from the circumstances that they had just went through they said to Jesus haven't you heard don't you know what just happened can I tell you something Jesus knows everything that happened and maybe you are that person that's watching right now that's been abandoned by your father mistreated by your mother you've gone through different circumstances choices in your own life have run you through the muck Jesus knows but he shows up right at your right hand and he says will you walk with me will you allow your circumstances to melt so that you can experience the joy of my presence and at the moment the Bible says there in Luke when they realized who it was Jesus, Jesus vanished from their midst and they said to one another didn't our hearts burn as we walked and talked with him along the way right now some of your hearts are burning because you're sensing the presence of God and you know that it's time to fully enter into that presence and to welcome that presence into your own life and shortly we're going to give you an opportunity to do that but right now I want you to just enjoy that presence let the presence of Jesus Christ let the fullness of his joy begin to eradicate everything that's happened to you everything that didn't happen to you all your disappointments all your unmet expectations right now you know there's so many things so many things that so many people go through and the enemy just uses them to block them from seeing the presence of God but right now the fullness of his joy is just washing over you so that you can experience that fullness that peace as he walks alongside of you oh it's such a great thing Pastor Gary it is so how do you stay in his presence well it says that God inhabits he lives and dwells in the praises of his people number one go to church get under that corporate anointing yes number two turn on Christian television where you can hear Christian music turn on Christian radio you know play a Christian music if you're in a hospital or a nursing home or if you're in jail get access to some Christian music sing, sing praises to the Lord don't let the enemy steal your song or another way to just stay in his presence is just listen to Pastor Rebecca as she sings for us we need a miracle you're the same God today and the same God tomorrow help me see the victory you already see let my faith be today what it will be tomorrow when I see the victory you already mountain and remember we're going to throw a piece of bread some juice tell us how you love to just take Holy Communion with us on move your mountain every week we've been looking at Psalm 16 together I encourage you to just delve into it it is so rich and so revelatory Jesus says that or the God says that he delights in you think about that you're his excellent one and I want you just to get that healthy image that right image of your heavenly Father and if you haven't believed that if you think either God's mad at you or you're not worthy enough or somehow you've messed up too much you need to just ask the Lord to set you free Pastor Maher I know that's a prayer God wants to answer absolutely to be free there's nothing like being free in him God wants you to be free Jesus said I came that they might have life and that they might have it more abundantly God wants your life to be abundant so if you are living beneath your privilege God is calling you today to allow him to move it out of the way so that you can be totally free and enjoy what Jesus did at the cross we're going to commemorate that I love taking communion also when we come together because it causes me to remember God wants us to remember what he wants to do for you and it's very easy to remember what has happened to you it's very easy to remember negative things but right now as you're watching this program I want you to take a moment I want you to think back to the time when you gave your life to Jesus I want you to consider the circumstances that you may have been in I want you to think of what it felt like as his spirit entered your heart and you were born again I want you to think of that moment I want you to treasure that moment because for some of you it's been a long time since you've thought back to that moment and the devil is coming he's just piled tragedy on top of tragedy disappointment on top of disappointment and God is wanting you right now to remember back to that time when you gave your life to him when you realized you were his you realized you were loved you realized you were accepted you realized that there is now no condemnation for those who are in Christ and you felt freer than you've ever been you may have cried you may have shaken you may have wept you may have shouted for joy you may have just sat and humble Thanksgiving now if you don't have that moment in your life some of you right now you're watching and you're searching when was that moment I don't know if that moment ever happened well you know what let's make right now your moment let's make today watching move your mountain be the moment when you've experienced for the first time the fullness of the joy of the full presence of God alive inside of you say how do I get there what do I do well it's as simple as this you first have to acknowledge that you're a sinner what does that mean you're a bad person no it means you're far from God the gradations of sin whether it's murder or a little white lie all of them just the smallest bit is enough to have you sent when you die but you know what the act of Jesus Christ on the cross is more than enough to wash away all of the sins no matter how many or how bad but you have to say I'm far from God I'm a sinner I am desperate need to be brought back into right relationship and then you understand that the only way to be brought back into right relationship with the fathers through the son Jesus who came to live that sinless life that none of us could live died the death that all of us deserved and then rose again from the grave to prove as a testimony to the world he is who he says he is the Lord and savior of the universe and you accept Jesus as your Lord and your savior you say I put my faith I put my belief not in my own efforts not in what I did do but in what he's already done I put my faith in the work of Jesus Christ on the cross I put my faith in his resurrection from the dead put my faith in him as Lord and savior and I turn from my sinful life and turn and receive his holy life and if you do that today's your day and so right now as you begin to turn your heart to the Lord I just invite you to just pray a prayer you can pray with me in your heart or you can pray the words that I pray and just say Lord Jesus I thank you today that you are who you said you were the Lord and savior of the universe and for the first time I give my life to you I acknowledge my sinfulness I acknowledge my desperate need and my distance from the Father and I turn to you to bring me near to him now I put my faith and hope and trust in you as God and savior and I surrender my life to you I surrender to your Lordship I turn from my sin and I yield to your Lordship right now God and I thank you today for seeing something in me worth dying for and I thank you today for giving me the opportunity to rise again with you in Jesus name Pastor Rebecca we talked about how the Lord is close to us as our right hand in his presence his presence is not a feeling it's a fact it's the truth and we need to grasp a hold of that because many times when you're feeling down you're saying well God's not near me he's not around me or when you're feeling like you've been neglected you're saying God's not with me but when you feel those goosebumps on a Sunday morning of worship oh he's right there no God is with you at all times his presence is with you at all times no matter if you feel it or you don't feel it it is there with you no matter where you are you can't escape from it psalmist david said in Psalm 139 whether I make my bed in hell or I go to the highest heavens Lord you are there he is there at all times with you recognize him we need to understand that and recognize that his presence is not leaving us we can turn our back on him but he's not going to leave us well we're going to take holy communion if you have your elements would you get them now let's pray over them the Bible says examine your own heart and Lord it was on the night that you were soon about to be betrayed you had us on your mind and you took bread you blessed it and broke it your body was broken for us for you were wounded for our transgressions you were bruised for our iniquities the chastisement of our peace was on you Lord and with and by your stripes we were and we are the healed and as you take that cracker that wafer that piece of bread eat of it now and be healed in the name of Jesus Christ of Nazareth we thank you for the blood we thank you we remember now the blood that takes away it was shed for the remission of our sins we thank you God we thank you for giving your only begotten son that because we believe that you've accepted us in the beloved so we say thank you for the blood we say thank you because you didn't have to do it but you did and we give you glory for it we give you all the honor for it in Jesus name alright take your cup now and drink and be washed and cleansed by the blood of the Lamb well the Bible says sin separates us from God and when we've confessed our sins talk about a great time to experience his presence just right now amen amen and just receive it right now just receive it remember I love to help Pastor Gary said it's not a feeling it's a fact so whether you're experiencing something physically or not I want you to mentally apprehend the reality the fact that his presence is with you right now you know I'm sitting here with Pastor Myer Pastor Gary Pastor Rebecca they could all turn their back on me they wouldn't see me anymore but that didn't mean that I went anywhere and the same way Pastor Rebecca said we can turn our back on God but that doesn't mean that he went anywhere so just receive the goodness of his presence right now come up inside of you and take the fullness of joy that inhabits it because his delight is in you yeah yeah well if you are blessed by programs like move your mountain you know we need your partnership to be able to continue to bring these programs to you I don't want you to ever take for granted that you're going to turn on your TV and we're always going to be there many are for the last 44 years every day 24 hours a day 365 days a year we're not commercially underwritten so we need partners that will invest whenever God gave Norma our founder the vision for this ministry she said Lord where am I going to get all the money I will give you partners that have the money and if you've never given to cornerstone television or maybe it's been a while I'd like to invite you to come home you could do a one time gift or a monthly gift pray about it let me give you our address it's cornerstone television network CTVN we're at one signal hill drive we're in wall Pennsylvania 15148-1499 and as you so I want you to know that cornerstone television is good ground and fertile soil and we thank you so much for your gift well we're going to go now to Pastor Rebecca as we head over to the altar she's going to sing for us holy spirit spirit goes where he's invited amen and we invite him here I pray that you are inviting him into your life into your homes into the situations that you are facing because he is in the midst today speak life today speak life speak life no matter what's going on speak life into your circumstances into your situations because our God is right there in our right hand waiting just to move on your behalf speak life over your children there it is there it is that's right that's right and you know the reality of it is you might not see life what you're speaking life over but that's what faith is it's the substance of things hope for and the certainty of what we don't see and so when you speak life as you were saying that Pastor Maher I thought of the parable Jesus says in Luke 18 when the Son of Man comes will he find faith on the earth this is the faith that I believe he's looking for not just faith in him he's looking for that but he knows those who are his but I believe he's looking for those who are his his excellent ones his sense to speak life to move and to operate in faith and to unite your faith together with other believers so that you can see breakthrough in your life well as you could see this altar is filled with many of you that's alright there's no distance in the spirit we say that all the time because it's true so just join your faith right now it's faith that pleases God we're going to pray as you agree with us Pastor Maher would you speak in for us thank you Lord Father we thank you for the privilege and the honor to come boldly to the throne of grace to get help to find mercy in our time of need and so we lift every single prayer request we lift up everyone who has anything that they need and done in the name of Jesus by faith calling it done because your word has said it is so and so we say thank you we say thank you amen would you slip over to the piano and just lead us in some worship please Father we just thank you so much for who you are you are a mighty God you are the only one who is able to see every one of these needs and be able to do something about them and so God that's why we come to you today because you are all sufficient God you are all powerful God and we recognize that in our lives those that are watching they recognize that in their lives Lord God that's why they've called in that's why they've written in and so God we bring these requests before you God those that are those are some of the prayer requests that are laid out before you right now God those that are feeling fear and anxiety they don't know what tomorrow's going to hold for them and so they're fearful of that that is the needs that are here today God and Lord I thank you that you break every fear you break every anxious thought Lord Jesus I pray that you would give those that are feeling with anxiety right now the ability to capture every thought who they are in you that you are their protector you are their sustainer you are their provider Lord Jesus God I pray that today that they would see your miraculous touch of healing of deliverance Lord of freedom Lord intervening every one of these needs and every one of these lives that are represented here today God you do your powerful and mighty work and we will thank you and praise you for it in Jesus name Oh God and we thank you today that Christ are a new creation and God we thank you right now that as our faith builds and as our desire for your presence increases that your joy will increase in our lives and so God I pray right now in Jesus mighty name for every body that is experiencing discomfort that right now the comforter himself the Holy Spirit would come and bring comfort and peace into those tremors right now Lord God whether it's from medication whether it's from age whether it's from nerve disorders we speak healing right now in Jesus mighty name we speak to wombs right now to be opened and to bear children we call upon life to spring forth in families who are praying and believing for babies in couples who are trying Oh God to bring forth life Lord God I pray right now when we release your anointing upon them to be fruitful and multiply to fill the earth and subdue it and to have dominion because that is both your first blessing upon mankind and your first command and we thank you God that we get to experience your presence we get to experience your nearness we get to experience your joy because God you are at our right hand and we are at yours and we thank you for that in Jesus' name Amen Amen Well we hope you were blessed and encouraged by today's program Pastor Myers just going to lead us in a time of worship stay in his presence Winnerstone television exists to spread the good news through Bible based programs and a fully staffed prayer line through CTVN lies are saved hearts minds and bodies are healed and Jesus is lifted high we can't do this work without you would you consider sending a gift this month to keep the gospel moving forward with power when you give we'll send you listen love repeat which presents scriptural examples of those who lived alert including Jesus who noticed those who least expected to be seen gives creative ideas for showing love to friends and family suggest practical ways to reach out to the 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I just announced to announce Natalia from University of Minnesota, who will speak about disorder and perhaps been like this. Thanks Laura. Good afternoon to everybody and let me continue saying that it's great pleasure to be here and thanks for organizers to give me the chance to present our work. Maybe as you can guess from the title of my talk, I'm going to talk about the interplay of some randomness which can, which exist in all the materials and some quantum fluctuation which bring the system and probably some quantum disorder state and the playground which I'm going to discuss is there. So today I have spin liquid which was very nicely introduced on the tutorial yesterday by hanging. So with that, let me start. So quantum spin liquid, the definition, the most robust definition of the state is a negative one. This is the state which doesn't break any symmetry and does not order. So basically in the quantum spin liquid we do have intrinsic disorder. And this is one of the, probably the prototype of the quantum spin liquid is there are under some violence bond state the so resonant violence bond so state which was proposed in 1973 by Anderson. So we see that the state is the super position of covering in this case of the triangle and that's why I'm not saying what is the model behind the state. So it's a triangle that is covered by various position of this spin singlet, and the state is the super position of this singlet, perhaps only nearest neighbor one, or maybe it has all possible lens the singlets of all possible lens. So, these are what we mean by intrinsic disorder, which might happen in a quantum spin liquid. So once we go to the lab or somebody is going to the lab, Gersh goes to the lab. So, then, in any real material, there is some randomness and this randomness in the form of extrinsic disorder can come in all possible ways. There can be some impurities it can be some defect in the lattices it can be some bond disorder. So, whatever it is so and sometimes we see that the system in which there is a lot of disorder does not order, but then the question is, is it spin liquid or not. What happens if we take the really beautiful pure material which is in the quantum spin liquid state. Imagine that we have one, and then we put by hand some randomness in this material. So what it will do we would kill that quantum spin liquid state with support the quantum spin liquid, what will happen so and basically that is what we are going to discuss today. Okay, so my playground is a catastrophe liquid and I will tell you later how we can apply this playground to some real materials, and very very briefly just to set the notation. So with this Hamiltonian we have a honeycomb two dimensional lattice and on each bond only one component of spin is interacting while people was so interesting at this model because it's exactly solvable. This seminal paper like say guitar showed us that we can find this beautiful exact solution by representing each spin degrees of freedom with the help of my run the parents, and it's also clear even from the classical theory that it's very difficult to satisfy all the bonds that it will be this money for the degenerate state from which we can construct this superposition which will be at the end, the quantum spin liquid, which is not a product state, but should be as a superposition so this is my kind of very brief introduction to quantum spin liquid but now I want to discuss some characteristics of this guitar spin liquid and that the easiest can be done through the excitations. So, and this is from the paper I have referenced some of it's not seen now so once again, if we try to understand this quantum spin liquid state in terms of the spin is very complicated. So using this my run a representation from a key type, we now can see what are these fluxes and fluxes are the spin, spin flip fractionalized into a fluxes which are static and gap excitation and my run a permanence, which are the dispersive mode. So, in this mode we do have a fractionalized excitation and that is the means how we can actually study this, the property of this spin liquid state. And what is also important and related will be important that if we flip one spin, then we will create two fluxes on the nearby surface. And another thing what I will need for my later discussion is how I characterize this excitation so basically, once again since I'm going to discuss this order. Let me first say when I'm going to high temperature and I will show another plot for this, then, despite the fact that this gap and static fluxes, then, above certain temperature which will call flux gap. I will go to the random flux sector, but at the zero temperature. Leap theorem tell us that the system in the zero flux sector, meaning that all these plaquette operator, which are conserved quantity and which are the reason why the model is exactly solvable has a value one. So, in this sector we can discuss the thermionic excitation, what is plot here is the density of states for the my run a permanence in this zero flux sector so if I'm talking about thermionic excitation, I'm talking about excitation inside the same flux but I can also consider going from one flux sector to another flux sector, and then I can define what is the flux gap. So, if I put the energy scale on the vertical axis here. So, and then that would be the energies, the fermionic energies in different flux sectors. I can define what is the fermionic gap like from the ground state to another or what is the energy of the fermionic excitation. I have time to go so if I'm inside. This, this is basically the key trial triangle so if all my couplings on x y and z bonds are equal to each other or almost equal to each other so if I'm in this part of the parameters space then I have a gapless fermionic liquid. Then I can also define. So I go from one sector to another, and my flux gap can be either very small or very large so I will use this terminology, thermionic excitation and flux gap later on so I just wanted to introduce this notation. And as I said, our fractionalization differ at zero temperature, and at finite temperature so if we are very low temperature because flux excitation that gap. So there is a low temperature, the excitations are mostly this my run a thermons and the situation is very close to the graphene physics, and then at the temperature around 10% of the guitar interaction. I go over to the, to the face, in which I have a random fluxes. And then I still have some in this in this random flux of sector. I have this my run a thermons and then of course, there is a once all the fractionalize excitations are excited. At the energy scale which is my th, which is of the order of key type interaction, then finally I'm going to conventional paramagnetic state and then there is no sense anymore at this temperature there is no sense anymore to talk about the fractionalize excitations. And that was all the theory at the beginning, and then, once again, I'm not going to discuss it in detail but studying from 2009 from the paper of jacquely and halloween, where they told us a recipe how, how to make these materials. This field become very active it has both experimental pattern theory, and people. It's become really the field, which maybe one can call key type of material. And once again what is the microscopic mechanism, you need a spin orbit coupling in order to have key type interaction it. There are also other non key type interaction and once again, in the tutorial yesterday hanky discuss this in detail. So what I want to sell with this that we do have materials so after this are 13 years. Basically, the list of material is very long and crystal growers are telling us, often, how we have a new materials which might be a candidate material. At the beginning, so the study started with the sodium and lithium irradiate materials, and then of course this alpharotenium chloride, which is the most studied key type materials. So, all these materials order at low enough temperature. We know that because of this non key type residue and actually which are probably smaller than key type interaction. And that's why we are calling the key type materials are materials in which key type interactions are the dominant direction. So from this plot from the review of he did a copy and others that in all these materials except one, and this is the last one I'm going to talk in more details about thermodynamic quantities show some transition present and basically the low temperature face is, is magnetically ordered. So people start trying to see how to kill this residual interaction and how probably find the two key types in liquid with no longer in shoulder. And then there's another list of materials. And this is once again the second generation of key type material this idea to go first and the second generation is taking from this paper of Simon traps. So these second generation of key type materials are more disordered. So it's clearly there is a disorder there. And at least, we can say for sure about this hydrogen and the collated lithium ready that this material does not order down to very low temperature so it does have disorder because this position of this hydrogen atom, they are in between the layers so it's not in this honey between, but their positions are not at all well defined so there is certain disorder, and people from the beginning understood that this the absence of the long range order is related to this quench disorder. And then the question is it just this ordered magnet or it is in liquid. And once again so this is the material of interest. So, in short, this material does not order at least down to 0.05 Kelvin, but it also have some divergent specific heat at the low temperature which actually tell us that there is some pile up of low energy states. And once the magnetic field is applied to this material. In this case it's applied along one one direction. So, this upturn of this, the suppression of this upturn in the lower temperature. The upturn is suppressed very very quickly with the very small magnetic field. And in addition, there is probably some scaling behavior so that was very interesting data and many people look to the disorder in this particular material trying to answer to the question. So, what is this a Kitayev still liquid. But I think in all these lists and maybe I need some work, and works I'm sorry, in that case. So the people asked the question, starting from the earlier work of John Jolket group. So, what disorder does for the Kitayev skin liquid behavior. So, and that we also look to that so basically let me tell about our contribution what I'm going to talk today, the driving force behind this especially numerical calculation is of my student then Hong Kong was in the University of Minnesota and absolutely bright day. So, let me first say how we describe disorder in the Kitayev skin liquid. So this is the pure model so basically, you have here different colors which correspond to x, y and z type of the bond. So, as I said, if you go above certain temperature, then you have a soup of different flux configuration in the pure Kitayev model they're still static. And basically, one of these configuration is shown here. So, the thermal disorder is a particular characteristic of the Kitayev skin liquid. And in that we can engineer different types of disorder for example we can look to the bone disorder. So some bones here, shown in the zero flux can be weaker or stronger than the remaining both. But we can also introduce a certain number of the vacancies or quasi vacancies. In that case, there will be a certain density of the sites, which would be either completely decoupled from the rest, or will be very, very weakly coupled and in that case we talk about not vacancies but quasi vacancies. And at the end of my talk, if I have time I will also talk about the strong disorder. And what kind of effects we are going to look surprisingly or maybe not surprisingly in this Kitayev skin liquid, the concept of fractionalization actually bring together different ideas of Anderson. We can look for Anderson localization in the Majorana fermions. And basically that comes together with the idea of the state which cannot be written as a product state. But we can also look to the leafships they also this all this kind of localization phenomena can be studied in the Kitayev skin liquid. And also, if we're looking to the strong disorder, probably we can look to some critical phases and some universal behavior. And of course, these order can induce a particular flux structure. Okay, so let me start with the weak disorder and compare two different type of disorder. So when we have a bone disorder and decide disorder, and you will see that in this case, we have completely different behavior. So when we are doing Kitayev, his original paper I just rewrite the Hamiltonian in terms of the Majorana fermions, and that is a straightforward way of doing. And this is just the Kitayev model. And the second term is the way how we can perturbatively describe the effect of magnetic field which break time reversal, and they will have for the students here just have next slide to explain how to obtain this term. Okay, the disorder is introduced here in the model. So now we have this j i j which depends on the bond. And with that, we can mimic any type of disorder which we want we can either have a binary bond disorder, or we can also do a uniform bond disorder when the bond is kind of distributed. And we can also divide all the sites into sites which are not connected to the vacancy and those which are connected to the vacancy and basically put his here this interaction j prime, which for vacancies simply zero, and for vacancy vacancies significantly smaller than j. So this is just one slide how this free spin interaction turns is appearing in the Kitayev model so you start with magnetic field which is, in this case in one one one direction. And then you treat that this Hx is small compared to the Kitayev interaction but what is more important that it's small compared to the flux, get the energy which goes to create fluxes in the lattice. And then what you do you just apply this term one after another, each spin clip introduced two fluxes. So if I apply Sigma X here then Sigma Y here and then Sigma Z here, then I'm going from the zero flux back to the zero flux. So, and this is basically the leading term in this perturbation what I have here in terms of the minor unfairness. Now I have a second neighbor hoping and these models now with the presence of couple look very much like how they model. What it does for so it doesn't change the flux sector if we start from the zero flux sector we remain in the zero flux sector. If we start for a particular vise and crystal so a particular flux configuration, we still remain in this flux configuration, but what it does for minor unfairness in the zero flux sector for example, just open the gap. So we will use it later so I just want to show how it. So the problem is, now, once we have this disorder, we cannot momentum is not any more good quantum number because translational symmetry is broken, and therefore we should do all the diagonalization finding the eigen energies at a finite system. Luckily, it's just a hopin Hamiltonian it's not so difficult and we can go to rather big system and basically, we can diagonalize this Hamiltonian in the real space using single value decomposition. Now, we can rewrite the diagonal Hamiltonian in terms of the complex fermion, but here and is not the momentum, but it's simply all this eigen energy in a given flux sector. So, now, how we started this order. Okay, so basically, let me start with a bond disorder. So, and in this case, as I said, I can look to a certain number for bonds which here is written by raw. It's like a binary disorder. And on a certain density of bonds, I can either put J prime which is smaller than J. And in this case, I dope my system with the weak bonds, or with the stronger bonds like J code to where all the rest bonds is equal to one. So what is important here is the density of states, and on the background, you always with the dashed line, you see the density of states for the pure kittles model. And you can see that, in principle, at least by looking to the density of states. Okay, so what is depopulated the states at the bump hope singularity is depopulated and somewhat distributed in the energy. So if I have the strong bonds, then I have more state at the higher energy, but overall, one can say that if this order is pretty weak, then this modification of the state is not that strong. Okay, so this is just the density of states and the blue color here means that I compute everything in the flux, zero flux sector. So, this is reasonable at temperature below the flux gap. I can also compare for the bond disorder this for the random flux so when I go to the temperature above this energy scale, and I consider, once again, that the probability for each packet to have either WP equal to one or minus one or equal to all these random flux. And then I can see that all these features in this random flux goes away. Okay, so the reason why I do not compare it with any other kind of flux configuration only zero flux or random flux. Once you have a bond disorder locally, your flux gap can be very small. And basically, the transition from zero flux to random flux is happening pretty fast. It can only tell me about the state it doesn't tell me about the way functions are there localized or not localized. So, and for that we can, we can introduce another quantity, which can illustrate the localization and that's usually done with the help of inverse participation ratio this PN, PN is computed for each eigen mode and, and here I is the summation oversight. So this inverse participation ratio, if we have a delocalized mode, then we will have a contribution, a small contribution here from many, many different sites. And then you'll see that this PN will scale as a one over and because and many sites are contributing where and scales with the system size. And that would be very small, however, if we do have a localized mode, then this PN would be larger so if we have just one stated would be just PN would be equal to one, or in any case that would be significantly larger value kind of order of one. And here this IPR inverse participation ratio everywhere is shown by red, and you can see that if we have a bone disorder, then, even if we have some low energy state low energy states remains delocalized in all possible cases. We do see that this, especially when we doped with the stronger, stronger bonds, we see that IPR is significant on the tails, and that is in fact what is called the listed sales, when the states at the age of the band becomes localized. So here's just a comparison of IPR for weak bond and strong bond cases. So here we have 10% of the weak bonds and, okay, so there is no listed sale there is no localization here. And that is, if we take, for example, one of the high energy modes from that area. So, since the majority of bonds which contributes to the density of states here they are coming from the strong bonds, which are the majority, then these bonds can be easily delocalized. However, if I doped with the strong bond so here it's J prime equal to two. If I take the state from close to the age, then this state has their mostly dominated by this weak bonds with the strengths are equal to two, but they are surrounded by the weaker bond, and that leads to the localization to localization. So it's kind of very intuitive way to understand why these states are more localized.  Similarly effect was also the coalition sales but if you go back to original Anderson model about the localization, then he also mentioned this. Okay, so this is about the bond disorder. In any case what you saw that you don't have a pile up of the low energy states in this case. Maybe you see some only if you consider the random flux configuration. But now I want to consider the side disorder. And basically I want to consider my back again he's the Hamiltonian where I divided into parts. This is for the bulk and this is basically for the states around the vacancies. And what do I see so around each of these vacancies. Once again this J prime is zero for the true vacancy and very small for the quasi vacancy. So first I have like either missing side or inside or very weakly connected side. And I have some mode which is localized on the opposite sub lattice so if this is a site that on the B sub lattice around this site. And basically which was shown first by the group of john Joker already in 2010. If you have a vacancy, then energetically it's prefer to attach the flux to it so that is called flux binding the energy load if you attach the flux to the vacancy. Okay, it's always what you do you always introduce the flux in the pairs. And in the ground state you will not be in the zero flux but you will be in the bound flux state. So now just to have this kind of color coding so blue is always for flux free orange is always for random flux and green I show for the case of their side disorder in the form of the vacancy. So here, for example we have the density of vacancy 2% here the 5% that is the case of the true vacancy. And here is the case of the quasi vacancy when J prime is equal just 1% of J, and I have 5% of the state. So immediately see that in this case, you have a pile up of the low energy state. Moreover, these states are localized so, or at least they are quasi localized and we need to understand this, what is this localization. So the spectrum weight is transferred from around the one whole singularity region, it's transfer both to the low energy region but also a little bit. So it's transferred to the low energy, but you also have localization so red is always the IPR. So you see that both the low energy states, and the state at high energy are quite low, quite localized. So, again, so this is delicious. And, once again when we talk about this quasi localization you see it's not one, it's large but not one. So, in fact, these low energy modes are only quasi localized, and they decay with a distance as one of our to the power alpha so it decays the way function decays when you go away from the vacancy. So, in fact, I can consider this vacancy also in the random, in the random flux. So basically I do not attach the flux to vacancy but I consider the random but that's why it's in orange. And then you see that in this case, the vacancy still give you some pile up of the low energy states, but they are not localized. Basically, we see that one ingredient which we need to explain this experiment and I will come to the experiment in the moment that the vacancy introduce a certain number of low energy states and these low energy states will be seen in the thermodynamics. So this is the conclusion of part one. And basically what I wanted to show that there are different type of disorder, side disorder, bone disorder and also thermal disorder. And once again in the Kitai quantum spin liquid, as I said before the ideas of quantum spin liquid and the one and one body Anderson localization kind of intertwined through the concept of spin fractionalization. And now basically what I am going to discuss, can we use this vacancies in order to explain experiment by Takagi when lithium adidate was intercalated with hydrogen. Okay, so here's just the collection of data. I don't know so maybe everybody saw this before, so many different type of experiment were performed and they're all reported in this, in this paper what is important that it's indeed an insulator. And you see this NMR there are no splitting or broadening down to the very low temperature, but also here you see in the NMR you also see that there is a low energy excited. And then, once again this particular Paulo divergence of the C over T in the specific heat, and some scaling behavior in the presence of the magnetic field. You can see how we can explain this with our theory. So, once again, let me consider now this 2% of the vacancy, and I can see that this bound flux bound to the backers. So then this is the density of states. So it's not really universal because the way how the slope is starting depends on the on the density, but I can clearly see that I have the corresponding upturn in the C over T. And what is important so it just basically comparing in this insert, what is compared is how the specific heat behave in their, in their pure model, and then how it behave in their bound flux. There's some questions so maybe you can read it to me but let me finish just this slide. So you see that this upturn you get both in the bound flux and in the zero flux. And once again it's how this upturn depend on the system size. And basically you can see that when you go to bigger and bigger system size, then the slope more or less saturate to, you can saturate to a particular value of like 0.5 which is very close to the experimental result. So what is the question. Yeah, the question is what is the physical significance of the random flux sectors at zero temperature. The ground state isn't zero. In zero temperature, there is none. So, in principle, you can think about the disorder but what is happening that in the cataract model we have all the flux sectors. So zero flux at the ground state and these random fluxes these are all different configuration these are excited states, but once you have a temperature, you can, your system is actually the soup of all these different configuration. In any case, we are interested in the term of dynamics so we need to consider what is the exciting stage of the model. Okay, so this slide is just to show that the vacancies are kind of good because once again flux sector is one thing, and also the density of boxes is a kind of the external thing which we control. But you can see that in all these three cases green that is the vacancy with the bound flux, zero flux and the random flux. You can see that you have upturned. So the question which you need to know to answer is how to suppress this upturned so what do you need what are the ingredients, you need to suppress this pile up of the low energy states in there. And here it becomes a bit tricky. So, one can do a very careful numerical study. And basically you can show that when you apply magnetic field and we always remained in the exactly solvable limit so we never say magnetic field we mimic it with effect of copper. And that is this free spin interaction which I show you before, because in that case the model remain exactly solvable. But you can see that here is the transition so when copper is growing there is a critical value of copper, where above which it's not anymore energetically preferable to attach the flux to the vacancy. So the system goes from the bound flux state to the zero flux state. So we just look in this particular kind of either in the bound flux state or in the zero flux state. We're now switching up copper. And what we see what copper does copper opens the gap in the bulk of the my run effluent. What we see here when we go down so these green once again it's a bound flux blue is the zero flux. What we see that the structure of the states are different in these two cases. And there's difference in the, in this in gap state in gap spectrum is actually responsible for for this behavior. And I would want to describe it in the middle. I don't know if there are more details, but you see that when we have a bound flux, we know when the time reversal symmetry broken, then for each flux in the time reversible in time reversal broken face, it will be a zero and this. Yes. And the zero mode is basically will be very important. Yes. You're back on the particle both. Yeah, it's remain my run effemence. I will always have particle false huge disorder with even disorder. And in my case, my physical states are actually I mean it's just shown here also so in the guitar model when you're dealing with my run effemence, you redefine your vacuum so in the vacuum, you feel all the states with the negative energy, and the excitation only with a positive energy because in my run fermions you have extended human space. So, but the particle whole symmetry remains all the time because my run effemence creation and regulation operator is the same so. I will just discuss, I will discuss the zero energy in the next couple of slides. Okay, so what I wanted to say that we do see this or if you follow my stars. So you do see that when copper is growing I should go from one sector to another, but you also see here that the. Basically, the idea is that once I have big enough copper. So, and my gap is big enough. What is responsible for the behavior in specific kid is what is the spectrum of this in gap state. And if I have a bound flux, because once I have a flux I have a zero mode, which will be broadening and I can show it in the like toy model. These states here would still give you some upturn, even when copper is growing, however, because when the copper is growing you have to go from this picture to that picture. And then you see that basically the absence of the zero mode in the zero flux sector. Actually, you start having some less and less state inside the gap. And the difference is once again, what are the low energy modes which we can see this so for each vacancy in the zero flux state. We have something what we'll call be this mode is like either the absence of this is the vacancy mode, which would be localized. And then we will have this mode, the peripheral mode, that's the same stories and graphene so, and these mode is only quasi localized. So once we have a flux attached to this, and this is our flux mode, then when copper is broken then we'll have additional low energy mode. So basically this is kind of this toy mode for explaining this in gap modes. So, again, so this is basically what is written here already said that I have these two different vacancy I have interaction between these low energy modes inside the vacancy. So I can, sorry, it's not really seen. But in case so this, I don't know how to remove this. Okay, maybe it's because here I remove everything so maybe I should also remove. Yeah, I want to remove because otherwise. Okay, in any case so what is written here, maybe the simplest isn't optional. Sorry. Just bring it up. And I will show play. Okay, so what I want to say that we can write the minimum or if the gap is large we just write everything at the energy scale below the gap. We can write what is the interaction between these modes inside the vacancy, and that is just proportional to this day prime, and that is the quantity which is basically it's zero if it's, if it's a true vacancy and it's very small, but I also have this coupling with this vacancy because all the vacancies are created in pairs, and this coupling is weak. It's weaker and weaker if the vacancies are further apart so it's proportional to one of them. Okay, so, and then, basically when copper is getting larger, what is happening this my zero mode is depopulated, and then I have only this interaction inside which is basically I have a gap so it's very difficult to communicate in between these two phases. So, and there is nothing to protect this zero mode and they become gapped because of hybridization. The situation is very different when I have a bound fuck, because now I have three degrees of freedom and I need to write this interaction inside the gap for these three different modes. So this zero mode, it's hybridized of course a little bit with another low energy mode. So it's broad and somewhat. So I do have a macroscopic number of these, I have some number of states around zero, and this state still participate in the thermodynamics so they should be seen in the thermodynamics. So in short, the answer is that the fact that the specific it's you were T is suppressed when we increase copper is because of two things. And because we have a transition from the flux three sector. So sorry from the bound flux sector to, okay, to the, from the bound flux sector to the zero flux sector. And then, once we go into this transition, then the structure in gap states changes. So, and once again, we look back to experiment, and we just compute this curve for different copper, and you can see that. Okay, so you suppress it, and then you have this behavior so which looks very similar to what was observed experiment. Not really exactly because couple of course is not the magnetic field, but assuming that copper is proportional to h cube, we can still try explain this scaling behavior. So I understand that I have only five. So, basically, I know that he did a colleague is not completely buying our theory and I don't really understand the reasoning. But I do think that this kind of vacancy of some sort of these local defects is actually if some reasonably some reasonable understanding of the experiment. So, we are kind of happy with that. Okay, so, let me, I have really few minutes but let me tell you where we were going recently from that so what I was telling before it's all about the week disorder. And then, by reading this paper from it a mark in Chi. So, at the same time they were also thinking about the same experiment. And they were thinking that, in fact, this kind of scaling behavior in the specific heat, which was seen in with the magnetic field can be understood with the help of the random singlet face. So we wanted to understand this. So first let me say that random singlet face. That is the face which naturally appears in the one D model in the disordered one D model and they were studied to death with the help of a real space, strong disorder and realization group. Basically, the idea is when you do dissemination when you get read at each step of iteration you get rid of high energy degrees of freedom at at the end you go to the low energy phase, where each side participate in the formation of the single. So, but, and basically in one day, that can be the exact solution. So, but a random singlet is not a quantum spin liquid and if something like this is happening here, then perhaps we should not talk about the guitar spin liquid. But we should talk about some strong disorder which leads to a formation of something which will understand in one day, and in 2D that's very difficult to study. So, with them, what we did we tried to look to the minimum model in which we can still study the physics of of the guitar model into the what do we need, we need to have one of the important thing for exact solution. So, we need to have this placate operate. And then we wanted to have something quasi one day that we can apply this strong to the disorder and realization group. And for that we just took a stripe of this honey combs. And basically, in order to, to employ the periodic boundary conditions in this direction so you need to add this additional coupling here. And then this stripe of the honey combs is nothing else as this letter, and the guitar model on the spin letter is exactly solvable you still have a placate operator, and placates are still exactly so. Basically, what we first look, and that is for the pure model, we look to the flux distribution flux gap distribution in this model. This is a honey combs model, and you can just put it jacks over jz here j y over jz. So, this is some sort of Kitayev triangle but computed for the flux degrees of freedom. And we computed also for the letter, and there is a certain similarity between the two so without okay so it's difficult to study this problem is difficult to study, but let us study the letter. There are two limits which we only managed to study. It's this xx limit. So here everything is in terms of jz. So, in the x limit j x and j y equal to each other. And in the icing limit we considered j y very small so these are two different limits. And really two minutes so what I need to say quickly is that the people before us in this in this paper they make wonderful transformation so there is a duality transformation which map this. So it's better to the one dimensional chain, but in this mapping so it's exact mapping what you have is now your placate operator this WL is inside the model. And this is already one D model and this is amenable to this strong disorder and realization group analysis. And skipping all the details. What I want to show is now you can in this model in this one D model you can study in these two limits at least you can study the scaling of the spin and floods gap. Again, I understand that I don't have time let me skip details and I have them in the conclusion. So, basically what is important there is another model one D model where you can study when you can apply this very well developed as the RG approach. And basically what you can see there that you have a spin gaps. So we look to the extreme statistic to the minimal spin gap and minimal flood gap. So, you can see that the spin gaps and floods gap. Remember my definition at the beginning of the talk. They show different type of the criticals they show some universal behavior in some cases, but this universal behavior depends are you looking for the spin gaps or you're looking for the flux gap. We cannot immediately extend our one day results to the to the result, but I think we can learn something. It's something non universal is happening at really low temperatures in this 2D, perhaps we can understand it with the help of this one day analysis. Okay, thank you very much for your attention. Thank you so much for your questions. So, the experiments then I reproduce by back and see disorder, no bone disorder.  I mean, in order to have this for this experiment you're talking about this, so you can still are somewhat explained with the help of the bond disorder but for these units to assume the random flux configuration. But if you have a random flux configuration that means that your flux gap is very small. It's not clear what protect quantum spin liquid, and is it really the spin liquid behavior or not in vacancies, the gap for the fluxes for most of the pocket is still the same flux gap so spin liquid behavior is preserved. Let me read. Okay, I just saw the, it's already disappeared. Okay. Please. No, we'll do it later so. Thank you, Natasha. I came in late so I may have missed this, but do you ever explore the possibility of non ergodic phases like glassy phases where the dynamics are frozen, because at least the phases that I heard about tended to be ergodic phases. I did not discuss dynamics at all so we only consider thermodynamics from the statistical point of view trying to explain this specific heat and so on so to some extent no. Okay, but in principle, you could have them in principle can have and you could have some very interesting glassy behavior. Okay, thank you. Okay, let me read the question. The question was, why in one day the random singlet phase is not a quantum spill liquid, because it's a product state. So basically the definition for quantum spill liquid is that it's a not product state. And here, even if you have all these different singlets, then, in any case you're writing the product state which is not a constant. Are there any other questions. No, that was the question. Okay. Okay, then let's thank Natasha again.


Dato Dewey here, back with some more Dragon Ball FighterZ rank matches, and today we are playing our Napa team.  I didn't mean to switch, so much for big Napa energy, that's done now, it's time to just move on, I'm redropping that dude, I'm on fire, I'm expecting a switch here, oh I'm switching again, if we ain't playing Napa, I don't want to clap this man, no I missed by a frame, I almost clapped this guy's side, don't switch me out, okay, he doesn't know Napa's the main, let me, let me serve you up something, I could have switched him out, that was one of my favorite things about Napa though, you've gotta block the nap, damn it, I dropped it again, oh I dropped it and side switched myself, unknowingly to me, oh nice heavy, I'm switching out, but you got too much health to lose, did we just run up in light jab, I think we did, let's go, is it gonna air level three, overhead, 6m doesn't work, 6m doesn't work but that's okay, he bounces back and we still take, we gotta get Napa back out here, I'm not feeling this Goku, I'm out, Napa overhead's coming in hot, oh I just level one, that's fine, we can still get the kill, but I'm really forgetting what I should go for after that, I think maybe a Cyberman plant into 2m, into 5 heavy I think, that might be what I should go for, and that's what we'll try next, snap me out, level three, damn he wants to mix, he's trying to make this Super Saiyan Goku comeback, he has the tools, that level three sparking is not a joke, is he going low or high, oh he's just gonna sit there, and I'm switching right back out, oh let me take you all, if you mind if I take you to the corner, get this man, Cyberman help, help, Cyberman help, get him, you just saw him, haha, no, I'm gonna armor through whatever he does next, if he gives me a small gap it's over, small gap, oh I'm sorry Napa, oh we're still out here, no I'm sorry again, I'm sorry I gave you false hope, haha, I'm sorry about the false hope more than anything else, practice, practice, this slight run up 2m, my man is has reads, okay, level three that might, no I don't think it'll kill, it'll do some damage for sure, now does he know I'm gonna spark here, is it too obvious, thought I had time, oh no he's about to make the comeback, that just snapped my confidence in two, my confidence does not exist anymore, and he's just back, back jump Super Dash, the bravest of choices, okay okay okay, we probably win here, don't make me level one to level three, you know I suffer, no it was only five, damn it, it's fine, it's fine, it's fine, we're scrubs, we're scrubs but we're scrubs with a win under our belt boys, let's do this, all right Napa you put in some good work but let's be honest, I expect more from you man, now we did start with a 5h last time and we're not gonna do that again, oh he just slapped me up, damn it, damn it, I should have respected that but come on, we all thought we was gonna mix this up and switch out, too much blue health, nice, that's gonna buy us a lot of time, especially when I drop it for the extra time, big IQ shreds, and Napa come out, finish the job, what play does Simon, get this man Simon, no he almost got the entire, that would have been so nice, I told him to do all lights so I probably should have mixed that up a little better, all right we get Goku back in here free, free look at all that blue health, I should have gone double lights into overhead, one level one for the kill, thank you very much, damn Napa is such a cool character, in this game, I'm not really a big fan of Napa in this show but oh we do it again, ah we shouldn't have done it again though, I just, I'm a, I'm prey to my urges dude, I just gotta get that out there, a 5h, come on, do we spark to save Napa, of course we do, oh don't kill me, please drop it, no, I also just remembered his Key Blast is really good, so I'll do that, I'll use that next time too, like I said there's so much to forget with Napa, I've forgotten more about Napa than I'll ever learn again, should have superdads, we're actually losing this game, the sparking's a pretty big deal, we have, no we didn't have advantage there, oh big to him, that's gonna let us get Yamcha out here just for the blue health of it all, I do want to try again, 1, 2, 3, 4, 5, maybe, maybe in a different universe I hit that, I'll take it, I'll take it, I'll take it, maybe should have gone with two level ones, now that I'm really looking at it, Goku kind of healed up all his blue health, but a knockout's a knockout, even though I could have done that a little more optimally, I just thought he was, you know he healed pretty fast, oh yeah that's bad for us, he might get a level three here, if that's what he wants, that's what I would recommend, another superdash, level three here, that's what's on the mind, no dude, I back dash, why do I always back dash at the last possible moment, where I just need to like back up a little and then die, whoa, whoa, whoa, that's not killing, that's not killing, oh that was aggressive, I felt the aggression in that one, wow we are, we are behind in a big way, that works, we were just lucky there, how many times are we gonna get lucky, we level three here because we kinda have to, and we have to read the sparking right, he would be brave not to spark here, so you know what the read is right boys, damn it, damn it, you know that Goku stuff is there, that's, oh that was, that was very Goku of me, and I appreciate that very much, come on Napa, can we see a little more Napa though, this time we just jump, jump back, oh was it too obvious, I mean the answer was yes, we clearly got punched in the face, oh I like that, I'll take that, I'll take that every day of the week, Napa just steamrolled them, Napa just steamrolled the boy, where are you going, where are you going when Napa's on the field, let me clap this man, we keep the same, I like the energy of Napa, oh get this man, Saibaman help me, Saibaman, Saibaman you know where to be, mid screen, where you at, no Saibaman cover me, cover me, cover me, no Saibaman I let you down, goodbye, I can still hear him down there, he's distraught dude, he's distraught, he never got to see his father, that's so sad, wow and we just lost our lead, I'm sorry Saibaman, we're punished for that, we're punished for that, yep, felt that one in my bones, no tech, oh it's it's always so obvious too, I don't know how I never get those, I guess that's what happens when your reaction time is pressed, I think we spark here, no DP, I'm very grateful, that was big, that sucked, oh but who really wins, did we level three, why not, why not, yeah I'm just pretty scary with the level three, do we read the sparking though, that's that's an interesting question, I'm gonna say no, I'm gonna say, I'm gonna have to say no to that one, I'm gonna have to say no, but I'm glad I thought of it because that either way, either way it happened I would have felt pretty okay with us, oh that's the second time that's happened, we weren't far back, no, oh keyblast just flat out aren't as good as beams, yeah it's punished, this is a punishment, he's got to spend some bar though, one bar will it be enough, no he wants to go with three, he also is not feeling it, I was like eh he can't spend one bar here, that's risky, how comfortable are you with the damage, show me the dragon rush already, show me the dragon rush, why are you hiding it, show me what I want to see, this is the level three hard knockdown, you know this is where, he can't kill us in the next hit, so either way we're gonna be okay, we're not okay, we're not okay, I know he still can't kill us but it's gonna hurt, he has to vanish, I don't know why he chose that route, that was interesting, we're punished, we're punished, we're punished, that was the obvious reaction for me, I should have mixed it up, oh man that was a good game, and after Napa's good start too, yeah yeah yeah yeah, you gotta read the flow, can we get one game, one more game please, thank you, I was a bit worried, at least let's finish this up, no nice super dash, switches out to Vegeta instantly, I wonder what the, he's feeling his Vegeta, I'll take it again, I'll take it again, Napa is the steamroller, you just can't guard against Napa, everything hits low these days, oh can I introduce you to my Hall of Fame, let me get him in the corner actually, that's probably the smart idea, Jesus, is this the power of the Super Saiyan, we don't, we don't spark, that was so obvious, did you guys see how it sparked up, and then like after five minutes had passed it was like, and guard cancel, make it a little more obvious next time fighters, my mind's telling me no but my body really did want to switch into Napa there, it would have been great, it would have been deluxe, but we gotta move past it, which Goku is me, I'm the purple one, wait I was not, maybe it was like I had already clicked the buttons but I swear I took my head off the controller, nose coming up, that's a free Napa switch and hold on, one, two, three, nicely done, nicely done, I appreciate it, level three is probably gonna come out, no he wants Goku, ah the beam, that was risky, that was a risky option, but it worked out, I down tech here every day of the week, curse these fat fingers I was born with, don't get three bars, goodbye Napa, may your soul find peace, again, oh what a mistake, I think it was because, oh, damn, can I get an F in the comments for Napa, I know I don't say that a lot but that's the 17th time this has happened, oh another input error, on my side, that should be the game, should be the game, should be the game, and it is the game, the Napa power hour ends with a three to one ratio, thank you to my opponents for the games, it was a lot of fun, we made a lot of mistakes with Napa, damn this is your fun character dude, I might have to play him again just for the fun of it all, but yeah let me know what your guys thoughts down below if you have a favorite moment, of course let me know down in the comment section as well, all of those things, thank you, how do I say thank you, thank you, there you go, but yeah let me know all your thoughts down below in one more, this dude, this dude knew, knew I was in an outro, but yeah here we are again, you thought it was over, but the curse of the rematch is still alive and well, not in great mood, nice, Napa steamroller back in action, haha dude, Napa is just the character that is so good at it, remind me not to do my outro again at the end of the video, or do we, what's the YouTube meta for what you did in outro, but now you have to do another one, oh man I think we spark here just for the, just for the, what is this, this is the most disheartened I've ever been, that's okay, that's okay, we're gonna move on from this, that's when we got to clash, oh, oh, oh, oh god this sucks, and then no, no dragon rush, am I finished, big punish, okay back it up, key blast, keeping, keeping comfortable, oh I could have done something a little better, a little better, not too much better, I tried jumping, I tried the jump, the jump ain't working out, dude, I am just bad at timing these jumps, I tried jumping forward, that just lowered my guard, now I get comboed, Jida's just kind of wasted there, oh it was an air too heavy at the, no, oh we are just losing our minds, nice, nice change, that was crazy, crazy lucky on my part, nicely done on the stagger, the 5H connects, and it's an easy take out from there, we have sparking still on our block, try to go for the cross up, down goes Goku, the health difference here, I think we're actually, yeah we're far below him, but the sparking should make up that difference, EX legs, three bars as well, this is the hard knockdown, yep and Vegeta also has a DP, so we're, we are not sparking here, wow that was lucky, big hit, four bars, could this be the end, I don't want this to be, no, no, no, no, down heavy punish, no he doesn't do it, we take the rematch win as well, get him out of here, very close to that last match, but yeah, like I was saying before that rematch, thanks for watching the comments stuff, all that stuff, but while you're down in the comments, make sure you hit the like button and subscribe if you did enjoy the video, we also have more videos up on your screen right now, if any of those catch your eye make sure to check them out as well, other than that, I've been Datu Joya, thanks so much for taking the time out to watch this video, and I will see you in the next one.


What's up guys Michael here with Jaspies and happy Saturday. I know you're not used to seeing me here It's used to You used to seeing Jason, but he decided to go to Dominican Republic. So you're stuck with me today First break of the day. We've got 2023 Bowman's Best University football breakers delight two box break It is a random first name first letter Thank you to Nicholas and Shane They are the two people that got into the break got their names and got the letters here Gonna roll the dice two and a three five times one two three four and five There we go five times got Shane down to Shane You guys in here and again five times for the letters as well one two three four and five L and N down to K Here we go. So let's pop these in here a little nicer We'll make it a little bigger for you guys too. Well Shane and Nicholas if you guys want to trade any letters, we'll give you guys A minute or so to see if anyone wants to trade but I'm gonna pause the video and Be right back if and we'll see if there's any trades. All right. We are back Looks like no deals. We're done. I printed out my list here the official list. Oh This is good. This is good. I have to remember to flip it The official list Thank you guys That's it. Let's just get into the break sounds good Eric This is my first time opening Bowman used best football. I've been dying to rip this after seeing What everyone else has been pulling but I am not too familiar with the configuration of the Product but I guess we'll just just go like this Good luck guys Harold Perkins Those are Jordan Travis are these all this is number. No, it's not number. Oh It is on the front to 25 That's Jordan Travis that goes to Jay, which is Shane Caleb downs at a 150 that goes to see which is also Shane his last spot mojo's spot Then we've got Mario Williams to 75 going to M. That's for Nicholas a little close Next up Justin Haynes to 99 Spot J. That's Shane as well And our first autograph here is going to be Chris Vizina Refractor autograph quarterback from Clemson spot see that's going to Shane with his last spot mojo Tried to teach Joe that top loaders on the left side were a lot easier Joe doesn't need teaching has been doing this long time as our first autograph second auto is a It's like a wanted poster Kyle McCord What are these called? Gunslingers and bandits. That's pretty cool 33 out of 50 That's an awesome card. Okay. That's going to Shane Not not a left-handed top loaders, but having the top loaders on the left side of the Left side of me makes it a little easier to grab them Just preference, you know We had it Eric, but nobody was buying it. So In the last autograph, I think it's three autos, right? I can't pick it up Is going to be Drew Allard 19 out of 25 want to spot D That is for Nicholas Great looking cards. Like I said, I posted another one if anyone wants to Try another one of these breaks I sit there And we've got a masterpieces bonix 47 out of 50 that goes to spot B Just Shane and the last card here is going to be Olufashanu Out of 50 for spot. Oh, which is Nicholas Yeah, I'm excited. I it was funny because we didn't get it to like two weeks after it came out so I guess people on that side were Bowman you doubt, I guess That was only box one. This is a fun stuff kid club Nick Phil Maffa 1099 green mini diamonds spot P is Nicholas the O and P spot Jaden Ott to 150 for J That's for Shane Yeah, all the mock drafts I see For this draft, he's he's up there grant Wells to a hundred that's for spot G That's for Shane. I haven't even seen hobby. I've only seen breakers the light of this. We've got a Javante Barnes for spot J Shane That is eight out of 99 This is a little bit of a troll looks like a Superfracture kind of from afar just like the color six out of 75 ties Simpson quarterback from Alabama Spot T is Nicholas. I'm liking what I see Like in what I see next Michael Penex 28 out of 50. How about that spot M? That's going to Nicholas. I would imagine some of them I mean they have like Shaddour and Travis Hunter in this right there. I don't think they're in this trap kid club Nick Patch an autograph. Is this numbered or no? I guess not but spot C. That's for Shane That is really thin a lot better than it looks And then we got fusion J.J. McCarthy It's like a puzzle piece. Whoa and That's a what's his name? Why can't I remember his name the running back quorum, right quorum His degree once he does that he'll decide And feel play football again use the rest of his eligibility interesting All right in the last part of the break Paris Jones to 50 It's for spot P.  That was sorry. Thanks for bearing with me there my first time ripping that so I was a little confused, but Do a little recap for you guys some nice color for Shannu Nick's Williams Jordan Travis to 25 Jane and ah and then the hits Drew Allard 25 Zena Kate Clubnick Michael Penex to 50 and Ty Simpson. All right. That does it my first break back on YouTube But Yeah, thanks everybody. Thank you to Nicholas and Shane who got into the break. Thank you guys for watching Like I said, I did post another one if anyone wants to get into another break like this, but I'll see you guys in the next one Bye guys


Okay, so let's start with this equation here, this balanced equation, so it's already been balanced for you. So you know it's an equilibrium equation. Why? Because you got the equilibrium error there, okay? So if you were to ask to write the expression for the equilibrium constant, that just means to write what the equilibrium constant would be. Don't put numbers in or anything like that, so the expression, right? So k e q, remember, equals the concentration of products that are in gashes or aqueous form over the concentration of reactants, both raised to their coefficients, okay? So here on the product side, we've got one gas, ammonia, or NH3, and it's going to be raised to the second power there, okay? So it's going to be squared. And we're going to divide that by the molar concentration of nitrogen gas, and then multiply that by the concentration of hydrogen gas raised to the third power, okay? So that would be the equilibrium constant. If you were given numbers for these concentrations, you could actually put them into the equilibrium constant and solve it, and we'll do that in a second, okay? So if there are any questions about this one, we'll do one more of these. They're pretty straightforward, so we'll do one more.


Hi everyone, Joe for jazzy's casebreaks.com coming at you with 2018 2019 chronicles basketball hangar box number 37 ranting number one, which at the end of the break You can be a can be a winner of those $465 random number block spots top two will re-randomize at the very end of the break as always We're gonna do the break itself first big. Thanks all of these folks right here. They're the teams there Let's roll it. Let's randomize it four and a four eight the hard way hard eight one Two after eight times Dustin down to Ben eight times for the teams Seven and eighth and final time But the Boston Celtics down to the Warriors Quinn I've worked at Jasper's for about six years now Five and a half years. I think that's what it is. There's the first half of the list right there Remember this is 2018-19. So Who has Dallas basically? There they are Ryan H. All right. Let's alphabetize this by team actually Hawks to Sean Maddox Hawks. All right, let's print. Let's rip We do not take playlist requests. I'm afraid BD. Oh, thank you. So there's the final print out right there the quick little break and Then we'll re-randomize that list and we'll see who's gonna get into that number block break There's Yannis on to decumpo honey walkers not too bad either. Those rookies will ship. There's Deandre Aitman Spellman Gary Clark. There's a Luka Donchich this is Just panini basketball addition Luka Donchich. I think I've seen one of these in a little bit. I mean, this is chronicles I'm not sure what designed there redoing All right, that's for Ryan H and the mouse Not too bad. Now. Let's see who wins those those other spots We've got Sean down to Patrick Let's roll it let's randomize it four and a five nine times for that list Top two after nine we're gonna are gonna get into that random number block. Good luck one two three four Five and ninth and final time after nine Patrick K. You saw your name right there Steven K down to Ryan H Apologies. Thanks for getting in appreciate you giving it a shot You saw that being teased right there Patrick K There you go. You're in the number block randomizer and Mike G in the number block randomizer So congrats to the both of you. Thanks for watching. Thanks for breaking with us, everybody I'll see you next time on jazby's case breaks.com. Bye. Bye