Correlation energy beyond Hartree-Fock selects valley polarization when valleys are related by n-fold rotation (n>2) or mirror, and spin polarization when they are related by time-reversal or C2, independent of most band details.
For example, this is the case for two valleys with anisotropic parabolic disper- sions εk,α = kT M −1 α k 2 , arising from band minima at the Brillouin zone (BZ) edges, as e.g
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Symmetry-determined generalized ferromagnetism in multi-valley electron fluids
Correlation energy beyond Hartree-Fock selects valley polarization when valleys are related by n-fold rotation (n>2) or mirror, and spin polarization when they are related by time-reversal or C2, independent of most band details.