Optical Su-Schrieffer-Heeger model in Honeycomb Lattice using DQMC

A great deal of research has occurred around electrons in a two-dimensional honeycomb lattice, spurred on by the synthesis of the single layer graphene, the discovery of unusual quantum hall effect in 2005, and unconventional superconductivity in graphene superlattices. In many of these systems, the electron-phonon interaction is thought to play a role; however, nonperturbative simulations of such interactions remain relatively sparse in the literature. In this study, we consider the optical Su-Schrieffer-Heeger model on Honeycomb Lattice, where the phonons are defined to live on the sites. Using a state-of-the-art DQMC code with HMC sampling for the phonon fields, we study the model in the weak and strong coupling limit with both (realistic) phonon energies and in the anti-adiabatic limit and find evidence for the formation of a robust bond-ordered phase near half-filling.