Efficient simulation of moire materials using the density matrix renormalization group

We present an infinite density-matrix renormalization group (DMRG) study of a model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction, tBLG is difficult to study with standard DMRG techniques—even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian. We focus mainly on the spinless, single-valley version of the problem where, at half filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics.