Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene

9 pags., 7 figs.We implement a self-consistent Hartree-Fock approximation based on a microscopic model in real space, which allows us to consider the interplay between the Hubbard and the extended Coulomb interaction in twisted bilayer graphene at the magic angle. These two interactions tend to favor different symmetry-breaking patterns, therefore having complementary roles in the regimes where one or the other dominates. We show that, for sufficiently large values of the on-site Hubbard repulsion, magic angle graphene has an antiferromagnetic ground state at the charge neutrality point, while at half filling of the lowest valence band the state becomes fully spin-polarized. In general, a suitable screening of the extended Coulomb interaction is required to observe the magnetic state in either case, as otherwise the instabilities take place in the charge sector, preferentially in the form of time-reversal, chiral, or valley symmetry breaking.This work has been supported by MINECO (Spain) under Grant No. FIS2017-82260-P, MICINN (Spain) under Grant No. PID2020-113164GB-I00, as well as by the CSIC Research Platform on Quantum Technologies PTI-001. The access to computational resources of CESGA (Centro de Supercomputación de Galicia) is also gratefully acknowledge