Topological phases of the interacting Su-Schrieffer-Heeger model: An analytical study

TL;DR

This paper analytically investigates the topological phases of the interacting Su-Schrieffer-Heeger model, revealing how electron-electron interactions modify the topological invariant and the charge of excitations using field theory methods.

Contribution

It provides an analytical framework linking the polarization density to topological phases in the interacting SSH model via Green's functions and low-energy quantum field theory.

Findings

Polarization density describes topological insulating phases.

Interactions modify the effective charge of excitations.

Two contributions to charge: quasiparticle renormalization and soliton topological charge.

Abstract

The interacting SSH model provides an ideal ground to study the interplay between topologically insulating phases and electron-electron interactions. We study the polarization density as a topological invariant and provide an analytic treatment of its behavior in the low-energy sector of the one-dimensional interacting SSH model. By formulating the topological invariant in terms of Green's functions, we use the low-energy field theory of the Thirring model to derive the behavior of the polarization density. We show that the polarization density in the continuum theory describes the usual topological insulating phases. Still, it contains an extra factor from the fields' scaling dimensions in the low-energy quantum field theory. We interpret this as a measure of the modified charge of the new excitations in the system. We find two distinct contributions: a renormalization of the electronic charge $e$ of a Fermi liquid because of quasiparticle smearing and an additional contribution coming from the topological charge of the soliton arising in the bosonized version of the Thirring model, the sine-Gordon model.