Kekul\'e valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene

Understand

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 Kekul\'e pattern.
• Finite size scaling reveals that the phase transition of the semimetal to Kekul\'e valence bond solid phase is continuous and belongs to chiral XY universality class.