Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models

Abstract

We exhibit a mapping identifying Kitaev's quantum double lattice models explicitly as a subclass of Levin and Wen's string net models via a completion of the local Hilbert spaces with auxiliary degrees of freedom. This identification allows to carry over to these string net models the representation-theoretic classification of the excitations in quantum double models, as well as define them in arbitrary lattices, and provides an illustration of the abstract notion of Morita equivalence. The possibility of generalising the map to broader classes of string nets is considered.

8 pages, 6 eps figures; v2: matches published version

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Cited by in corpus (52)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Classifying quantum phases using Matrix Product States and PEPS
• The Quantum Double Model with Boundary: Condensations and Symmetries
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Generalizations and limitations of string-net models
• Full Dyon Excitation Spectrum in Generalized Levin-Wen Models
• A hierarchy of topological tensor network states
• Cage-Net Fracton Models
• Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
• Fusion basis for lattice gauge theory and loop quantum gravity
• Ground State Degeneracy in the Levin-Wen Model for Topological Phases
• Methods for simulating string-net states and anyons on a digital quantum computer
• Kitaev's quantum double model as an error correcting code
• Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries
• Electric-magnetic duality of lattice systems with topological order
• Topological phases from higher gauge symmetry in 3+1D
• Quantum gravity kinematics from extended TQFTs
• Kitaev lattice models as a Hopf algebra gauge theory
• Topological Disorder Parameter
• Probing topological order with Rényi entropy
• Revisiting Entanglement Entropy of Lattice Gauge Theories
• Microscopic description of 2d topological phases, duality and 3d state sums
• Kitaev models based on unitary quantum groupoids
• Mapping between Morita equivalent string-net states with a constant depth quantum circuit
• Kitaev's Lattice Model and Turaev-Viro TQFTs
• Hopf algebra gauge theory on a ribbon graph
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• A Defect Verlinde Formula
• Generalized Toric Codes Coupled to Thermal Baths
• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras
• From 3D topological quantum field theories to 4D models with defects
• Boundary and domain wall theories of 2d generalized quantum double model
• On weak Hopf symmetry and weak Hopf quantum double model
• Generalized Color Codes Supporting Non-Abelian Anyons
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• 2D Quantum Double Models From a 3D Perspective
• Fracton-like phases from subsystem symmetries
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• From entanglement renormalisation to the disentanglement of quantum double models
• Topological and nontopological degeneracies in generalized string-net models
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case
• Electric-magnetic duality and ${\mathbb{Z}}_2$ symmetry enriched Abelian lattice gauge theory
• Poisson-geometric analogues of Kitaev models
• Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• Local topological order and boundary algebras
• Simplicity condition and boundary-bulk duality
• Partition function of the Kitaev quantum double model
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries