Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model

TL;DR

This study uses quantum Monte Carlo simulations to explore phase transitions and exotic phases in a two-dimensional Su-Schrieffer-Heeger model, revealing novel flux behaviors and phase transitions driven by electron-phonon interactions.

Contribution

It introduces a detailed phase diagram of the 2D SSH model with electron-phonon coupling, highlighting emergent gauge theories and flux phenomena, and characterizes phase transitions between VBS and AFM phases.

Findings

Emergent $ ext{Z}_2$ gauge theory with flux $ eq 0$ in assisted-hopping regime.

Direct, continuous transition between VBS and AFM phases with increasing phonon frequency.

Finite-temperature pseudogap phase related to nesting instability at large hopping.

Abstract

We study a Su-Schrieffer-Heeger electron-phonon model on a square lattice by means of auxiliary-field quantum Monte Carlo simulations. The addition of a symmetry-allowed interaction permits analytical integration over the phonons at the expense of discrete Hubbard-Stratonovich fields with imaginary-time correlations. Using single-spin-flip and global updates, we investigate the phase diagram at the O(4)-symmetric point as a function of hopping $t$ and phonon frequency $\omega_0$. For $t=0$, where electron hopping is boson assisted, the model maps onto an unconstrained $\mathbb{Z}_2$ gauge theory. A key quantity is the emergent effective flux per plaquette, which equals $\pi$ in the assisted-hopping regime and vanishes for large $t$. Phases in the former regime can be understood in terms of instabilities of emergent Dirac fermions. Our results support a direct and continuous transition between a $(\pi,0)$ valence bond solid (VBS) and an antiferromagnetic (AFM) phase with increasing $\omega_0$. For large $t$ and small $\omega_0$, we find finite-temperature signatures, a disordered pseudogap phase, of a previously reported $(\pi,\pi)$ VBS ground state related to a nesting instability. With increasing $\omega_0$, AFM order again emerges.