Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Soft sym- metries of topological orders
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Twin phases are inequivalent phases sharing a generalized charge under symmetry S, enabling stable direct transitions without spontaneous symmetry breaking even after gauging.
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.
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
citing papers explorer
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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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.
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Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.