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

The fascinating quantum many-body states in twisted bilayber graphene (TBG) at magic angle, due to the interplay of Coulomb interactions and the quantum metrics of flat bands, have been well understood both experimentally and theoretically. However, the phase diagram and excitations as functions of twist angle and permittivity are still largely unknown. Here, via a newly developed momentum-space continuous-field quantum Monte Carlo method fully taking into account long-ranged Coulomb interactions and flat bands' quantum metrics with system sizes that were not accessible before, we show that charge-neutral TBG realizes an angle-tuned quantum phase transition from a gapped Kramers intervalley coherence (KIVC) state to a Dirac semimetal with critical angles around 1.2$\deg$. In single-particle spectra we demonstrate the evolution of a minimum gap at $\Gamma$ at the magic angle and towards touching points at Brillouin zone corners as the angle increases. The free energy and KIVC order parameter show that the transition belongs to fermionic Gross-Neveu criticality, and is robust upon varying the permittivity or the interlayer hopping.