Fermionic Monte Carlo Study of a Realistic Model of Twisted Bilayer Graphene - Hofmann, Johannes S.; Khalaf, Eslam; Vishwanath, Ashvin; Berg, Erez; Lee, Jong Yeon (Physical review. X, 2022)
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality. We establish the absence of a sign problem for this model in a momentum-space approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion. Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a “pseudogap” regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature. Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.