For the cocycle to define a valid modulated SPT phase, it must be invariant under the translation action, i.e.,ω(g, h) =ω(t(g), t(h))

Classification To evaluate the strong index of the SPT phases protected by the exponential symmetry, consider the group cohomology of the internal symmetry,H 2(Gint, U(1)), which

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Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints

cond-mat.str-el · 2026-03-19 · unverdicted · novelty 7.0

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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Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints cond-mat.str-el · 2026-03-19 · unverdicted · none · ref 2
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.

For the cocycle to define a valid modulated SPT phase, it must be invariant under the translation action, i.e.,ω(g, h) =ω(t(g), t(h))

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