Twin phases are inequivalent phases sharing a generalized charge under symmetry S, enabling stable direct transitions without spontaneous symmetry breaking even after gauging.
Morita equivalence of pointed fusion categories of small rank
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We classify pointed fusion categories C(G, $\omega$) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita equivalence classes are distinguished by the set of the indicators and ribbon twists of their Drinfeld centers. In particular, the modular data are a complete invariant for the modular categories Z(C(G, $\omega$)) for |G[< 32. We use the computer algebra package GAP and present codes for treating complex-valued group cohomology and calculating Frobenius-Schur indicators.
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cond-mat.str-el 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
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Twin Phases: Phase Transitions Without Hidden Symmetry Breaking
Twin phases are inequivalent phases sharing a generalized charge under symmetry S, enabling stable direct transitions without spontaneous symmetry breaking even after gauging.
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Twin Algebras: Condensable Algebras beyond Anyons
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.