Anyon condensation and tensor categories

DOI10.1016/j.nuclphysb.2014.07.003zbMath1325.81156arXiv1307.8244OpenAlexW2038255126MaRDI QIDQ894708

Liang Kong

Publication date: 23 November 2015

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.8244

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Topological field theories in quantum mechanics (81T45)

Related Items (51)

Classification of \(\mathfrak{sl}_3\) relations in the Witt group of nondegenerate braided fusion categories ⋮ Gapped boundary theory of the twisted gauge theory model of three-dimensional topological orders ⋮ Generalized ADE classification of topological boundaries and anyon condensation ⋮ Computing defects associated to bounded domain wall structures: the $\mathbb{Z}/p\mathbb{Z}$ case ⋮ On the classification of topological orders ⋮ Level bounds for exceptional quantum subgroups in rank two ⋮ Defects in the 3-dimensional toric code model form a braided fusion 2-category ⋮ Entanglement entropy of topological orders with boundaries ⋮ Hamiltonian and algebraic theories of gapped boundaries in topological phases of matter ⋮ Boundary-bulk relation in topological orders ⋮ Boundary and domain wall theories of 2d generalized quantum double model ⋮ Non-invertible Gauss law and axions ⋮ Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries ⋮ A mathematical theory of gapless edges of 2d topological orders. I ⋮ Categories of quantum liquids. I. ⋮ Constructing non-semisimple modular categories with local modules ⋮ A lattice model for condensation in Levin-Wen systems ⋮ Ishibashi states, topological orders with boundaries and topological entanglement entropy. I ⋮ Anyonic exclusions statistics on surfaces with gapped boundaries ⋮ Higher gauging and non-invertible condensation defects ⋮ Dynamical Abelian anyons with bound states and scattering states ⋮ Duality defects in \(E_8\) ⋮ On weak Hopf symmetry and weak Hopf quantum double model ⋮ Gapped interfaces in Fracton models and foliated fields ⋮ The boundary phase transitions of the 2+1D \(\mathbb{Z}_N\) topological order via topological Wick rotation ⋮ Fibonacci-type orbifold data in Ising modular categories ⋮ \(\mathbb{Z}_N\) duality and parafermions revisited ⋮ When does a three-dimensional Chern-Simons-Witten theory have a time reversal symmetry? ⋮ Gapless edges of 2d topological orders and enriched monoidal categories ⋮ On continuous 2-category symmetries and Yang-Mills theory ⋮ Gauging noninvertible defects: a 2-categorical perspective ⋮ Prime decomposition of modular tensor categories of local modules of type D ⋮ \(U(1)\) spin Chern-Simons theory and Arf invariants in two dimensions ⋮ A mathematical theory of gapless edges of 2d topological orders. II. ⋮ Symmetries and anomalies of \((1+1)d\) theories: 2-groups and symmetry fractionalization ⋮ Boundary Hamiltonian theory for gapped topological phases on an open surface ⋮ On finite symmetries and their gauging in two dimensions ⋮ Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries ⋮ Classification of topological phases with finite internal symmetries in all dimensions ⋮ Generalized global symmetries of \(T[M\) theories. I.] ⋮ Hopf algebra actions in tensor categories ⋮ Ishibashi states, topological orders with boundaries and topological entanglement entropy. II: Cutting through the boundary ⋮ Fusing binary interface defects in topological phases: The Z/pZ case ⋮ Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies ⋮ Erratum and addendum to: ``Anyon condensation and tensor categories ⋮ Domain walls in topological phases and the Brauer-Picard ring for \(\mathrm{vec} (\mathbb{Z}/p\mathbb{Z})\) ⋮ Galois orbits of TQFTs: symmetries and unitarity ⋮ One dimensional gapped quantum phases and enriched fusion categories ⋮ Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry ⋮ No-go theorem for boson condensation in topologically ordered quantum liquids ⋮ A remark on gapped domain walls between topological phases

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