Phase diagrams of trivial phases in class A non-interacting fermions exhibit topological textures from non-trivial state families, computed via higher Berry phases, with diabolical points hosting robust boundary modes.
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A Z2 x Z2 gauge theory on a 1D chain produces an LSM theorem in the Gauss law subspace via a U(1) symmetry from the constraint, forbidding trivial gapped states and identifying a gapless Dirac fermion point with r^{-2/9} correlations.
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Textured phase diagrams of featureless insulators
Phase diagrams of trivial phases in class A non-interacting fermions exhibit topological textures from non-trivial state families, computed via higher Berry phases, with diabolical points hosting robust boundary modes.
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Lieb-Schultz-Mattis theorem from gauge constraints
A Z2 x Z2 gauge theory on a 1D chain produces an LSM theorem in the Gauss law subspace via a U(1) symmetry from the constraint, forbidding trivial gapped states and identifying a gapless Dirac fermion point with r^{-2/9} correlations.