Twin phases are inequivalent phases sharing a generalized charge under symmetry S, enabling stable direct transitions without spontaneous symmetry breaking even after gauging.
Bogomolov multiplier, double class-preserving automorphisms and modular invariants for orbifolds
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abstract
We describe the group of braided tensor autoequivalences of the Drinfeld centre of a finite group $G$ isomorphic to the identity functor (just as a functor) as a semi-direct product $Aut^1_{br}(\Z(G))\ \simeq\ Out_{2-cl}(G)\ltimes B(G)\ $ of the group of double class preserving automorphisms and the Bogomolov multiplier of $G$. The Bogomolov multiplier $B(G)$ is the subgroup of its Schur multiplier $H^2(G,k^*)$ of classes vanishing on abelian subgroups of $G$. We show that elements of $Aut^1_{br}(\Z(G))$ give rise to different realisations of the charge conjugation modular invariant for $G$-orbifolds of holomorphic conformal field theories.
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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.
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.
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
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Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.