Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model

TL;DR

This paper uses quantum Monte Carlo simulations to study the 2D Su-Schrieffer-Heeger model, revealing a bond ordered wave insulator at half-filling and identifying a critical electron-phonon coupling for its emergence.

Contribution

First 2D quantum Monte Carlo study of the SSH model, clarifying the bond ordering pattern and phase transition characteristics.

Findings

Bond ordered wave insulator exists at half-filling in 2D

A critical electron-phonon coupling is necessary for BOW formation

Transition involves spontaneous ${\

Abstract

Over the last several years, a new generation of quantum simulations has greatly expanded our understanding of charge density wave phase transitions in Hamiltonians with coupling between local phonon modes and the on-site charge density. A quite different, and interesting, case is one in which the phonons live on the bonds, and hence modulate the electron hopping. This situation, described by the Su-Schrieffer-Heeger (SSH) Hamiltonian, has so far only been studied with quantum Monte Carlo in one dimension. Here we present results for the 2D SSH model, and show that a bond ordered wave (BOW) insulator is present in the ground state at half-filling, and argue that a critical value of the electron-phonon coupling is required for its onset, in contradistinction with the 1D case where BOW exists for any nonzero coupling. We determine the precise nature of the bond ordering pattern, which has hitherto been controversial, and the critical transition temperature, which is associated with a spontaneous breaking of ${\cal Z}_4$ symmetry.