Topological invariants in terms of Green's function for the interacting Kitaev chain

TL;DR

This paper investigates topological invariants in the interacting Kitaev chain using Green's functions, revealing new distinctions between phases and emphasizing the importance of dimerization in the charge density wave phase.

Contribution

It introduces a method to compute topological invariants via Green's functions for the interacting Kitaev chain, accounting for dimerization effects and identifying more phases than fermion parity alone.

Findings

Green's function approach captures topological phases in interacting systems.

Dimerization influences the calculation of topological invariants.

More topological phases are distinguished than by fermion parity.

Abstract

The 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 topological invariant in the charge density wave phase must consider the dimerized configuration of the ground states. The variation of topological invariant are attributed to the poles of eigenvalues of the zero-frequency Green's functions. For the interacting dimerized Kitaev chain, we show that the topological invariant defined by the Green's functions can distinguish more topological nonequivalent phases than the fermion parity.