The spin stiffness or spin rigidity is a constant which represents the change in the ground state energy of a spin system as a result of introducing a slow in-plane twist of the spins. The importance of this constant is in its use as an indicator of quantum phase transitions —specifically in models with metal-insulator transitions such as Mott insulators. It is also related to other topological invariants such as the Berry phase and Chern numbers as in the Quantum Hall effect.