A DMRG study of a lattice model for Twisted bilayer graphene aligned with hexagonal Boron Nitride

In this work, we study a lattice model for twisted bilayer graphene aligned with hexagonal boron nitride (TBG/hBN) at quarter filling. We employ the density matrix renormalization group algorithm in the matrix product state formulation (DMRG-MPS) to obtain the ground state of the system and study its phases. In agreement with previous experimental results, which showed a large anomalous Hall effect for the system, we find that strong interactions lead to spontaneous polarization in the spin/valley space, giving a Chern insulator. It is interesting to observe how this evolves as a function of the bandwidth, which can be tuned via the hopping parameters, as well as the interaction strength.