On a zero-field sphere, each angular-momentum shell behaves like a flat band with inversion symmetry, so a local potential creates equal density at opposite poles and projected interactions become long-ranged.
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Flat bands on spherical surface: from Landau levels to giant-quantum-number orbitals
On a zero-field sphere, each angular-momentum shell behaves like a flat band with inversion symmetry, so a local potential creates equal density at opposite poles and projected interactions become long-ranged.