Towards Non-Invertible Anomalies from Generalized Ising Models
arXiv:2208.09101 · doi:10.21468/SciPostPhys.15.4.150
Abstract
We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable -dimensional bulk models with noninvertible topology are constructed from the so-called generalized Ising (GI) models in dimensions. The GI models can then terminate on the boundaries of the bulk models. The construction generates abundant examples, including not only prototype ones such as toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the topological order, the 4d topological order with pure-loop excitations, etc. The boundary of the solvable model is potentially anomalous and corresponds to precisely only sectors of the GI model that host certain total symmetry charges and/or satisfy certain boundary conditions. We derive a concrete condition for such bulk-boundary correspondence. The condition is violated only when the bulk model is either trivial or fracton ordered. A generalized notion of Kramers-Wannier duality plays an important role in the construction. Also, utilizing the duality, we find an example where a single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders. More generally, topological orders may also be generated starting with lattice models beyond the GI models, such as those with symmetry protected topological orders, through a variant bulk construction, which we provide in an appendix.
arXiv commentpublished version, 17+18 pages, 5 figures
References in corpus (79)
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- Topological quantum memory
- Local stabilizer codes in three dimensions without string logical operators
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
- Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
- Models for gapped boundaries and domain walls
- Topological Defect Lines and Renormalization Group Flows in Two Dimensions
- A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
- Quantum codes on a lattice with boundary
- Topological quantum order: stability under local perturbations
- Condensate induced transitions between topologically ordered phases
- Quantized Thermal Transport in the Fractional Quantum Hall Effect
- Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
- Orbifold groupoids
- Protected edge modes without symmetry
- Topological boundary conditions in abelian Chern-Simons theory
- The Quantum Double Model with Boundary: Condensations and Symmetries
- Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
- Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
- Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
- Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
- Fracton topological order via coupled layers
- Foliated fracton order from gauging subsystem symmetries
- Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
- Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
- Anomalous Symmetry Fractionalization and Surface Topological Order
- Classification of Topological Defects in Abelian Topological States
- Glassy dynamics and aging in an exactly solvable spin model
- Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
- Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
- Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
- Strong-weak coupling self-duality in the two-dimensional quantum phase transition of superconducting arrays
- Commuting Pauli Hamiltonians as maps between free modules
- Universal topological phase of 2D stabilizer codes
- Glassiness and constrained dynamics of a short-range non-disordered spin model
- Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions
- Boundary-bulk relation in topological orders
- Cage-Net Fracton Models
- Symmetry as a shadow of topological order and a derivation of topological holographic principle
- Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
- Topological dualities in the Ising model
- Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions
- Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
- A mathematical theory of gapless edges of 2d topological orders. Part I
- Twisted foliated fracton phases
- Generalized ADE Classification of Gapped Domain Walls
- Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
- Fractionalization in Superconductor Josephson Junction Arrays Hinged by Quantum Spin Hall edges
- Microscopic definitions of anyon data
- Algebraic Methods for Quantum Codes on Lattices
- Braiding and Gapped Boundaries in Fracton Topological Phases
- Non-Abelian Hybrid Fracton Orders
- Gapless edges of 2d topological orders and enriched monoidal categories
- Anisotropic layer construction of anisotropic fracton models
- A mathematical theory of gapless edges of 2d topological orders. Part II
- A Generalization of Non-Abelian Anyons in Three Dimensions
- Plaquette Ising models, degeneracy and scaling
- Boundary Hamiltonian theory for gapped topological phases on an open surface
- Construction of Fractal Order and Phase Transition with Rydberg Atoms
- Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
- Geometric effects on T-breaking in p+ip and d+id superconductors
- One dimensional gapped quantum phases and enriched fusion categories
- A topological phase transition on the edge of the 2d topological order
- Microscopic description of 2d topological phases, duality and 3d state sums
- Categorical Symmetries at Criticality
- Entanglement bootstrap approach for gapped domain walls
- Trajectory phase transitions in non-interacting spin systems
- Mapping between Morita equivalent string-net states with a constant depth quantum circuit
- Boundary theory of the X-cube model in the continuum
- A Defect Verlinde Formula
- Fractal Quantum Phase Transitions: Critical Phenomena Beyond Renormalization
- A unified view on symmetry, anomalous symmetry and non-invertible gravitational anomaly
- Computing data for Levin-Wen with defects
- Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders
- Double semions in arbitrary dimension
- Gapped domain walls between 2+1D topologically ordered states
- Families of Gapped Interfaces Between Fractional Quantum Hall States
- Boundary Modes in the Chamon Model
Cited by in corpus (5)
- A Chern-Simons theory for dipole symmetry
- Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
- Additivity, Haag duality, and non-invertible symmetries
- Efficient Preparation of Nonabelian Topological Orders in the Doubled Hilbert Space
- Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries