Kekul\'e valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger Model and its relevance to Graphene

TL;DR

This study uses advanced quantum Monte Carlo simulations to explore how phonon interactions induce Kekulé valence bond order in a honeycomb lattice model, shedding light on phenomena relevant to strained graphene.

Contribution

It demonstrates the weakly first-order nature of the semi-metal to Kekulé valence bond solid transition and emphasizes the role of bond-stretching phonons in graphene-like systems.

Findings

SM-KVBS transition is weakly first-order at all temperatures

Graphene is close to the phase boundary in the phase diagram

Bond-stretching phonons are crucial for KVBS order formation

Abstract

We perform sign-problem-free determinant quantum Monte Carlo simulations of the optical Su-Schrieffer-Heeger (SSH) model on a half-filled honeycomb lattice. In particular, we investigate the model's semi-metal (SM) to Kekul{\'e} Valence Bond Solid (KVBS) phase transition at zero and finite temperatures as a function of phonon energy and interaction strength. Using hybrid Monte Carlo sampling methods we can simulate the model near the adiabatic regime, allowing us to access regions of parameter space relevant to graphene. Our simulations suggest that the SM-KVBS transition is weakly first-order at all temperatures, with graphene situated close to the phase boundary in the SM region of the phase diagram. Our results highlight the important role bond-stretching phonon modes play in the formation of KVBS order in strained graphene-derived systems.