Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach

TL;DR

This paper introduces a functional renormalization group method to analyze topological invariants in interacting fermion chains, specifically identifying phase transitions into the Haldane phase through Green function zeros, with results validated against DMRG data.

Contribution

The paper develops a novel functional RG approach to topological invariants in interacting systems and demonstrates its effectiveness in identifying phase transitions into the Haldane phase.

Findings

Transition to Haldane phase involves a zero of the Green function.

Phase boundary results agree quantitatively with DMRG data.

Method provides insights into topological phase transitions in interacting fermion chains.

Abstract

We present a functional renormalization group approach to interacting topological Green function invariants with a focus on the nature of transitions. The method is applied to chiral symmetric fermion chains in the Mott limit that can be driven into a Haldane phase. We explicitly show that the transition to this phase is accompanied by a zero of the fermion Green function. Our results for the phase boundary are quantitatively benchmarked against DMRG data.