The two-dimensional optical Su-Schrieffer-Heeger model: ground state and thermodynamic properties

TL;DR

This study explores the phase diagram of a two-dimensional optical SSH model, revealing various ordered phases and finite-temperature transitions using advanced quantum Monte Carlo simulations.

Contribution

It provides the first comprehensive analysis of the 2D optical SSH model's ground state and thermodynamic properties, highlighting novel phase behaviors and transition temperatures.

Findings

Identification of staggered and armchair VBS phases

Discovery of an O(4) antiferromagnetic phase

Higher critical temperatures for VBS transitions

Abstract

We investigate the two-dimensional optical Su-Schrieffer-Heeger (SSH) model, in which the electron hopping amplitude is modulated by the difference between neighboring phonon coordinates. Using sign-problem-free auxiliary-field quantum Monte Carlo simulations, complemented by mean-field analysis, we determine the long-range ordered phases as a function of the electron-phonon coupling and phonon frequency. By examining both adiabatic and antiadiabatic regimes, we reveal the emergence of staggered and armchair valence bond solid (VBS) phases, as well as the O(4) antiferromagnetic phase. In addition, finite-temperature simulations show that the VBS transition occurs at critical temperatures significantly higher than in models with local electron-phonon coupling, consistent with the presence of lighter polarons in the metallic regime. These findings establish the ground-state and finite-temperature phase diagrams of the optical SSH model, which emphasize its similarities and contrasts with other electron-phonon systems.