The 1D Ising model and topological order in the Kitaev chain

Abstract

We elaborate on the topological order in the Kitaev chain, a p-wave superconductor with nearest-neighbor pairing amplitude equal to the hopping term Delta=t, and chemical potential mu=0. In particular, we write out the explicit eigenstates of the open chain in terms of fermion operators, and show that the states as well as their energy eigenvalues are formally equivalent to those of an Ising chain. The models are physically different, as the topological order in the Kitaev chain corresponds to conventional order in the Ising model.