Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene

Using large-scale quantum Monte Carlo simulations, we exactly solve a model of fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.United States. Department of Energy (Grant FG02-03ER46076