Twin phases are inequivalent phases sharing a generalized charge under symmetry S, enabling stable direct transitions without spontaneous symmetry breaking even after gauging.
Computing modular data for pointed fusion categories,
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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.