I am working on twisted bilayer graphene (TBG) using momentum-space continuous-field quantum Monte Carlo (CFMC) and exact diagonalization (ED). Hamiltonian dynamics are incorporated into my Monte Carlo method, allowing us to simulate TBG systems with sizes up to 21×21—far exceeding the capabilities of discretized-field Monte Carlo methods (DQMC), which are limited to system sizes of at most 9×9. As a result, CFMC can be considered approximately 1000 times faster than DQMC for TBG simulations. For ED, in the case of pristine TBG, there are two good quantum numbers: momentum and Chern number. Using these two invariants, we can solve the ground state of a 6×6 TBG system via exact diagonalization.