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.
Lu, Lieb-schultz-mattis theorems for symmetry- protected topological phases, Annals of Physics470, 169806 (2024)
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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.