# Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators

## TL;DR

This paper develops a Green's function approach to study weakly interacting 1D topological insulators, confirming the robustness of bulk-edge correspondence and critical behavior even with interactions.

## Contribution

It introduces a formalism combining Green's functions and T-matrix techniques to analyze topological properties and edge states in interacting systems.

## Key findings

- Bulk gap closing remains a key feature at phase transitions with interactions.
- Edge states persist and can be characterized using the T-matrix formalism.
- Critical exponents of edge decay match noninteracting universality classes.

## Abstract

We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase transitions, and using interacting Su-Schrieffer-Heeger model as an example. From the many-body spectral function, we find that closing of the bulk gap remains a defining feature even if the topological phase transition is driven by interactions. The existence of edge state in the presence of interactions can be captured by means of a T-matrix formalism combined with Dyson's equation, and the bulk-edge correspondence is shown to be satisfied even in the presence of interactions. The critical exponent of the edge state decay length is shown to be affiliated with the same universality class as the noninteracting limit.