Anyonic Chains, Topological Defects, and Conformal Field Theory

Abstract

Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to an enormously rich (and largely unexplored) space of two-dimensional critical theories in the thermodynamic limit. One remarkable feature of these systems is the appearance of non-local microscopic "topological symmetries" that descend to topological defects of the resulting CFTs. We derive various model-independent properties of these theories and of this topological symmetry / topological defect correspondence. For example, by studying precursors of certain twist and defect fields directly in the anyonic chains, we argue that (under mild assumptions) the two-dimensional CFTs correspond to particular modular invariants with respect to their maximal chiral algebras and that the topological defects descending from topological symmetries commute with these maximal chiral algebras. Using this map, we apply properties of defect Hilbert spaces to show how topological symmetries give a handle on the set of allowed relevant deformations of these theories. Throughout, we give a unified perspective that treats the constraints from discrete symmetries on the same footing as the constraints from topological ones.

54 pages and 17 figures; v2: reference added; preprint number added; appendix B of v1 has evolved into a separate publication

References in corpus (11)

• Generalized Global Symmetries
• Interacting anyons in topological quantum liquids: The golden chain
• Duality and defects in rational conformal field theory
• A short introduction to Fibonacci anyon models
• Topological defects for the free boson CFT
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Collective states of interacting Fibonacci anyons
• Microscopic models of interacting Yang-Lee anyons
• The classifying algebra for defects
• Elaborating the phase diagram of spin-1 anyonic chains

Cited by in corpus (64)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• On finite symmetries and their gauging in two dimensions
• Non-Invertible Duality Defects in 3+1 Dimensions
• Higher Gauging and Non-invertible Condensation Defects
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Non-invertible Time-reversal Symmetry
• Topological Transition on the Conformal Manifold
• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Topological Operators and Completeness of Spectrum in Discrete Gauge Theories
• Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory
• Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Mapping topological to conformal field theories through strange correlators
• On lattice models of gapped phases with fusion category symmetries
• Probing symmetries of quantum many-body systems through gap ratio statistics
• Dualities in one-dimensional quantum lattice models: topological sectors
• Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States
• Bootstrapping Non-Invertible Symmetries
• Numerical evidence for a Haagerup conformal field theory
• Entanglement entropy in the Ising model with topological defects
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Topological field theories and symmetry protected topological phases with fusion category symmetries
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Fermionization of fusion category symmetries in 1+1 dimensions
• Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
• Topological aspects of the critical three-state Potts model
• Galois conjugated tensor fusion categories and non-unitary CFT
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Tensor network approach to phase transitions of a non-Abelian topological phase
• Entanglement entropy and negativity in the Ising model with defects
• Open spin chain realization of topological defect on 1d Ising model and boundary and bulk symmetry
• Operator fusion from wavefunction overlaps: Universal finite-size corrections and application to Haagerup model
• On weak Hopf symmetry and weak Hopf quantum double model
• Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
• Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models
• Boundary SymTFT
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• K-theoretic classification of inductive limit actions of fusion categories on AF-algebras
• MERA as a holographic strange correlator
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Quantum Electronic Circuits for Multicritical Ising Models
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• Anyonic Chains -- $\alpha$-Induction -- CFT -- Defects -- Subfactors
• Duality defect in a deformed transverse-field Ising model
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
• Dualities between 2+1d fusion surface models from braided fusion categories
• Lattice models from CFT on surfaces with holes I: Torus partition function via two lattice cells
• Local topological order and boundary algebras
• Les Houches Lecture Notes on Tensor Networks
• Self-duality protected multi-criticality in deconfined quantum phase transitions
• From gauging to duality in one-dimensional quantum lattice models
• Fibonacci topological phase in arrays of anyonic chains
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• A non-semisimple non-invertible symmetry
• A stabilizer code model with non-invertible symmetries: Strange fractons, confinement, and non-commutative and non-Abelian fusion rules
• Chiral Edge States Emerging on Anyon-Net
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling