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

TL;DR

This study uses quantum Monte Carlo simulations to investigate a honeycomb lattice fermion model with cluster charge interactions, revealing a continuous transition from semimetal to Kekulé valence bond solid phase relevant to twisted bilayer graphene.

Contribution

It provides the first large-scale simulation evidence of a continuous semimetal to Kekulé valence bond solid transition in an extended Hubbard model.

Findings

Identified a continuous phase transition in the model.

Characterized the transition as belonging to the chiral XY universality class.

Demonstrated potential relevance to twisted bilayer graphene physics.

Abstract

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.