Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene

We report an implementation of the momentum space quantum Monte Carlo (QMC) method on interaction model for twisted bilayer graphene (TBG). The long-range Coulomb repulsion is treated exactly with flat bands, spin and valley degrees freedom electrons taking into account. prove absence minus sign problem QMC simulation when either two valleys or are considered. By realistic parameters twist angle interlayer tunnelings simulation, we benchmark data exact band gap obtained at chiral limit, to reveal insulating ground states charge neutrality point (CNP). Then, Green’s functions from QMC, perform stochastic analytic continuation obtain first set single-particle spectral function TBG CNP. Our scheme therefore offers controlled computation pathway systematic investigation electronic in various electron fillings.