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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Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
Inserting a symmetry defect along the orientation-reversing cycle on a Klein bottle in a 2D Z2 SPT phase induces an extra ground state charge that persists at the transition to the trivial phase, causing exact two-fold degeneracy independent of system size.
citing papers explorer
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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.
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Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints
Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
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Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
Inserting a symmetry defect along the orientation-reversing cycle on a Klein bottle in a 2D Z2 SPT phase induces an extra ground state charge that persists at the transition to the trivial phase, causing exact two-fold degeneracy independent of system size.