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

Many strongly correlated materials are thought to be governed by the interplay of electron-phonon (e-ph) coupling and Coulomb interactions. Recent efforts have seen interesting phases from the combination of strong e-ph and e-e interactions. There have been relatively few studies focused on the interplay of the Hubbard model with an e-ph model which modulates nearest neighbor hopping integrals; namely, the Su-Schrieffer-Heeger model. Even fewer of these studies have been conducted in dimensions greater than one and most are focused on models in which the displacements independently modulate each hopping integral. We present a determinant quantum Monte Carlo study of the optical SSH-Hubbard model on a two-dimensional square lattice, where site-centered phonons simultaneously modulate neighboring hopping integrals. We present a low temperature phase diagram in the adiabatic regime with boundaries between antiferromagnetic Mott insulating and bond-order-wave (BOW) states, with a critical coupling required to stabilize the BOW phase. We find no evidence for superconductivity in the limit of small U.