Antiferromagnetism and Kekul\'e valence bond order in the honeycomb optical Su-Schrieffer-Heeger-Hubbard model

TL;DR

This study uses quantum Monte Carlo simulations to explore how electron-phonon coupling and Hubbard interactions influence phase transitions in a honeycomb lattice model relevant to graphene, revealing potential pathways to induce Kekule9 valence bond order.

Contribution

It provides the first detailed phase diagram of the oSSH-Hubbard model on the honeycomb lattice, highlighting the conditions under which Kekule9 valence bond order can be stabilized in graphene-like systems.

Findings

Weak to moderate Hubbard repulsion enhances KVBS correlations.

Graphene near the SM-KVBS phase boundary can be driven into the KVBS phase.

Increasing Hubbard or e-ph coupling favors KVBS over AFM phase.

Abstract

The precise role of e-ph coupling in graphene and related materials on a honeycomb lattice is not yet fully understood, despite extensive research on these systems. Here, we perform sign-problem-free determinant quantum Monte Carlo (DQMC) simulations of the optical Su-Schrieffer-Heeger (oSSH)-Hubbard model on the honeycomb lattice, focusing on the parameters relevant to graphene. Performing finite-size scaling analyzes, we obtain the model's ground state phase diagram, which includes the semi-metal (SM), Kekul\'e Valence Bond Solid (KVBS), and anti-ferromagnetic (AFM) phases, as well as indications of a small KVBS/AFM coexistence region. We find that a weak to moderate Hubbard repulsion, tuned toward the SM-AFM critical value in the pure honeycomb Hubbard model, enhances KVBS correlations and can even stabilize the KVBS phase. Estimating the effective parameters for graphene places it in the SM region of the phase diagram, but near the SM-KVBS phase boundary. Notably, we predict that increasing either the on-site Hubbard repulsion or the e-ph coupling strength drives graphene toward the KVBS phase rather than the AFM phase, highlighting a synergistic effect that can be exploited to further control the remarkable properties of graphene and related materials.