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.

• Received 11 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.121406