Chiral symmetry is a unitary operator S , that acts on c i , as a unitary rotation ( S c i S − − 1 = ( U S ) i j c j ,) and satisfies S 2 = 1 . A Hamiltonian H possesses chiral symmetry when S H ^ ^ S − − 1 = − − H ^ ^ , for some choice of S (on the level of first-quantised Hamiltonians, this means U S and H are anticommuting matrices).