Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study

Twisted bilayber graphene (TBG) has revealed fascinating quantum many-body states, and unstrained chargeneutral TBG at 1.08° is understood, both experimentally and theoretically , as a correlated insulator due to the interplay of long-range Coulomb interactions and the quantum metrics of flat bands. However, the fate of the ground state as one continuously tunes the twisted angle is still largely unknown. Here, theoretically, by employing a newly developed momentum-space continuous-field quantum Monte Carlo method that can fully take into account the long-range Coulomb interactions and quantum metrics of flat bands with system sizes that were not possible before , we show that charge-neutral TBG realizes an angle-tuned quantum phase transition with Gross-Neveu criticality at Θc ~ 1.20(1)°, from the analyses of single-particle spectra, free energy and the order parameter of inter-valley coherence. This shows the exciting possibility that by tuning away from 1.08°, pristine TBG can mimic a fundamental phase transition of Dirac fermions.