A comparative determinant quantum Monte Carlo study of the acoustic and optical variants of the Su-Schrieffer-Heeger model

TL;DR

This study uses determinant quantum Monte Carlo to compare acoustic and optical variants of the SSH model, revealing near identical results under certain conditions and highlighting differences in bond models affecting chain length.

Contribution

It provides a systematic comparison of SSH model variants, establishing conditions for their equivalence and identifying key differences in bond coupling effects.

Findings

Optical and acoustic models yield nearly identical results at half-filling when parameters are matched.

Bond model exhibits different behavior due to coupling with the $q=0$ phonon mode.

Chain length shrinks in the bond model but not in acoustic or optical models when coupling strength increases.

Abstract

We compare the acoustic Su-Schrieffer-Heeger (SSH) model with two of its optical variants where the phonons are defined on either on the sites or bonds of the system. First, we discuss how to make fair comparisons between these models in any dimension by ensuring their dimensionless coupling $\lambda$ and relevant phonon energies are the same. We then use determinant quantum Monte Carlo to perform non-perturbative and sign-problem-free simulations of all three models on one-dimensional chains at and away from half-filling. By comparing the results obtained from each model, we demonstrate that the optical and acoustic models produce near identical results within error bars for suitably chosen phonon energies and $\lambda$ at half-filling. In contrast, the bond model has quantitatively different behavior due to its coupling to the $q = 0$ phonon mode. These differences also manifest in the total length of the chain, which shrinks for the bond model but not for the acoustic and optical models when $\lambda \neq 0$. Our results have important implications for quantum Monte Carlo modeling of SSH-like interactions, where these models are sometimes regarded as being interchangeable