  We present an infinite density-matrix renormalization group (DMRG) study of
an interacting continuum model of twisted bilayer graphene (tBLG) near the
magic angle. Because of the long-range Coulomb interaction and the large number
of orbital degrees of freedom, 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 which we show is both efficient and accurate even
when including the spin, valley and orbital degrees of freedom. To benchmark
our approach, 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 opens up a new route for numerically studying strong correlation physics in
spinful, two-valley tBLG, and other moire materials, in future work.
