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.
We will now state the Fisher-Hartwig conjecture (see Ref
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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.