DQMC study of competing phases of the Hubbard-optical SSH model on the honeycomb lattice

Graphene is one of the most widely studied two-dimensional quantum materials and is known to host a variety of emergent quantum phenomena, such as relativistic fermions, quantum Hall effect, superconductivity, etc. In a previous determinant quantum Monte Carlo (DQMC) study, we examined the effect of electron-phonon (e-ph) coupling on the honeycomb lattice and demonstrated that this interaction can drive the formation of the Kekule valance bond solid (KVBS) state, which are commonly observed in strained graphene, for specific coupling and phonon frequency values. Here, we extend this study to include the interplay of e-ph interactions and Hubbard interactions. Specifically, we will study the Hubbard-SSH model on a honeycomb lattice using DQMC to treat the relativistic fermions and competition between KVBS, antiferromagnetism, and semi-metal phases on an equal footing.