A Green's function perturbation theory in the band basis gives analytical Hartree-Fock ground states for twisted bilayer graphene and shows self-consistent GW corrections reduce compressibility oscillations.
Examples are the quantum Hall state ˆγy, valley Hall state ˆτz ˆγy, spin-Hall state ˆσz ˆγy, and valley-spin-Hall state ˆτz ˆσz ˆγy
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Many-body perturbation theory for moir\'{e} systems
A Green's function perturbation theory in the band basis gives analytical Hartree-Fock ground states for twisted bilayer graphene and shows self-consistent GW corrections reduce compressibility oscillations.