Strong coupling phases of partially filled twisted bilayer graphene narrow bands.

States favored by Coulomb interactions projected onto the basis of the four narrow bands of the “magic angle” twisted bilayer graphene will be presented. Due to the unusual shape and symmetry of the Wannier orbitals [1], the resulting strong coupling problem is qualitatively different from the much studied (topologically) trivial narrow band i.e. a solid in an atomic limit. Instead, a dramatically new form of the interaction Hamiltonian is obtained [2]. It contains terms beyond the usual Hubbard term, leading to different strong coupling phases as in the atomic limit. Specifically, the usual anti-ferromagnetic super-exchange mechanism fails and turns ferromagnetic with an approximate spin-valley SU(4) symmetry.
Results of DMRG and variational trial state calculations will also be presented.

[1] Jian Kang and Oskar Vafek, Phys. Rev. X 8, 031088 (2018)
[2] Jian Kang and Oskar Vafek, Phys. Rev. Lett. 122, 246401 (2019)