# Is magic-angle twisted bilayer graphene near a quantum critical point?

## TL;DR

This study uses quantum Monte Carlo simulations on an extended Hubbard model to identify a quantum critical point related to symmetry breaking, which may shed light on phenomena in magic-angle twisted bilayer graphene.

## Contribution

It provides the first unbiased numerical evidence of a quantum critical point in a model relevant to twisted bilayer graphene, with precise critical exponents and phase transition details.

## Key findings

- Identification of a quantum phase transition from Dirac semi-metal to VBS insulator.
- Critical exponents consistent with 3D N=4 Gross-Neveu chiral XY universality.
- Discovery of two distinct VBS phases and their transition properties.

## Abstract

An extended Hubbard model on a honeycomb lattice with two orbitals per site at charge neutrality is investigated with unbiased large-scale quantum Monte Carlo simulations. The Fermi velocity of the Dirac fermions is renormalized as the cluster charge interaction increases, until a mass term emerges and a quantum phase transition from Dirac semi-metal to valence bond solid (VBS) insulator is established. The quantum critical point is discovered to belong to 3D $N=4$ Gross-Neveu chiral XY universality with the critical exponents obtained at high precision. Further enhancement of the interaction drives the system into two different VBS phases, the properties and transition between them are also revealed. Since the model is related to magic-angle twisted bilayer graphene, our results may have relevance towards the symmetry breaking order at the charge neutrality point of the material, and associate the wide range of universal strange metal behavior around it with quantum critical fluctuations.