A SymTFT-based classification of 1+1d mixed-state phases with non-invertible strong and weak symmetries, with explicit lattice-model examples.
Computing Modular Data for Pointed Fusion Categories
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abstract
A formula for the modular data of $\mathcal{Z}(Vec^{\omega}G)$ was given by Coste, Gannon and Ruelle in arXiv:hep-th/0001158, but without an explicit proof for arbitrary 3-cocycles. This paper presents a derivation using the representation category of the quasi Hopf algebra $D^{\omega}G$. Further, we have written code to compute this modular data for many pairs of small finite groups and 3-cocycles. This code is optimised using Galois symmetries of the S and T matrices. We have posted a database of modular data for the Drinfeld center of every Morita equivalence class of pointed fusion categories of dimension less than 64.
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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.
Adding 3-cocycle twists to elementary Abelian gauge groups raises the maximal total quantum dimension from square-root to linear growth in the rank cutoff, and new envelopes are proved for symmetric, alternating, almost-simple, solvable, and radical-free families.
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.
citing papers explorer
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SymTFT Approach for Mixed States with Non-Invertible Symmetries
A SymTFT-based classification of 1+1d mixed-state phases with non-invertible strong and weak symmetries, with explicit lattice-model examples.
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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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Maximal Total Quantum Dimension at Bounded Rank in Dijkgraaf-Witten Theories
Adding 3-cocycle twists to elementary Abelian gauge groups raises the maximal total quantum dimension from square-root to linear growth in the rank cutoff, and new envelopes are proved for symmetric, alternating, almost-simple, solvable, and radical-free families.
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Twin Phases: Intrinsic Deconfined Quantum Criticality
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.