Topological Invariants in Terms of Green's Function for the Interacting Kitaev Chain

A one-dimensional closed interacting Kitaev chain and the dimerized version are studied. The topological invariants in terms of Green’s function are calculated by the density matrix renormalization group method and the exact diagonalization method. For the interacting Kitaev chain, we point out that the calculation of the topological invariant in the charge density wave phase must consider the dimerized configuration of the ground states. The variation of the topological invariant is attributed to the poles of eigenvalues of the zero-frequency Green functions. For the interacting dimerized Kitaev chain, we show that the topological invariant defined by Green’s functions can distinguish more topological nonequivalent phases than the fermion parity. (paper)