Angle-tuned Gross-Neveu quantum criticality in twisted bilayer graphene

The quantum many-body states in twisted bilayer graphene at magic angle have been well understood both experimentally and theoretically. However, the phase diagram and excitations versus twist angle and permittivity are still largely unknown. Here, via a state-of-the-art momentum-space continuous-field quantum Monte Carlo method fully taking into account long-ranged Coulomb interactions and flat bands’ quantum metrics with system sizes up to 15 × 15, we show that charge-neutral twisted bilayer graphene realizes an angle-tuned quantum phase transition from a Kramers intervalley-coherent insulator to a Dirac semimetal with critical angles around 1.2°. Single-particle spectra demonstrate the evolution of the gap at Γ to touching points at Brillouin zone corners as the angle increases. The free energy and order parameters show that the transition belongs to fermionic Gross-Neveu criticality, and is robust upon varying the permittivity or the interlayer hopping.