Antiferromagnetic and bond-order-wave phases in the half-filled two-dimensional optical Su-Schrieffer-Heeger-Hubbard model

TL;DR

This study uses quantum Monte Carlo simulations to explore the phase diagram of a two-dimensional optical SSH-Hubbard model, revealing antiferromagnetic and bond-order-wave phases, with no long-range antiferromagnetism at zero Hubbard interaction.

Contribution

First non-perturbative determinant quantum Monte Carlo analysis of the 2D optical SSH-Hubbard model, uncovering its phase diagram and the conditions for different ordered phases.

Findings

Insulating antiferromagnetic Mott phase identified.

Bond-order-wave phase stabilized by critical electron-phonon coupling.

No long-range antiferromagnetism at zero Hubbard interaction.

Abstract

Electron-phonon ($e$-ph) interactions arise in many strongly correlated quantum materials from the modulation of the nearest-neighbor hopping integrals, as in the celebrated Su-Schrieffer-Heeger (SSH) model. Nevertheless, relatively few non-perturbative studies of correlated SSH models have been conducted in dimensions greater than one, and those that have been done have primarily focused on bond models, where generalized displacements independently modulate each hopping integral. We conducted a sign-problem free determinant quantum Monte Carlo study of the optical SSH-Hubbard model on a two-dimensional square lattice, where site-centered phonon modes simultaneously modulate pairs of nearest-neighbor hopping integrals. We report the model's low-temperature phase diagram in the challenging adiabatic regime ($\Omega/E_\mathrm{F} \sim 1/8$). It exhibits insulating antiferromagnetic Mott and bond-order-wave (BOW) phases with a narrow region of coexistence between them. We also find that a critical $e$-ph coupling is required to stabilize the BOW phase in the small $U$ limit. Lastly, in stark contrast to recent findings for the model's bond variant, we find no evidence for a long-range antiferromagnetism in the pure $(U/t=0)$ optical SSH model.