A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation

Abstract

We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a reduction of the discrete gauge symmetry with respect to the original systems, which corresponds to a generalized mechanism of explicit symmetry breaking. The topological order is either partially lost or completely destroyed throughout the various models. The new systems display condensation and confinement of the topological charges present in the standard non-Abelian Kitaev models, which we study in terms of ribbon operator algebras.

arXiv commentAdditinal figures, minor corrections

References in corpus (38)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• String-net condensation: A physical mechanism for topological phases
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Quantum Orders and Symmetric Spin Liquids
• An RVB phase in the triangular lattice quantum dimer model
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Information and Computation: Classical and Quantum Aspects
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Topological Order and Conformal Quantum Critical Points
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Entanglement purification and quantum error correction
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Simulation of topological field theories by quantum computers
• Implementation of Spin Hamiltonians in Optical Lattices
• Topologically protected quantum bits from Josephson junction arrays
• Fermions, strings, and gauge fields in lattice spin models
• Topological Computation without Braiding
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Quantum groups and nonabelian braiding in quantum Hall systems
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Fractionalization in the cuprates: Detecting the topological order
• Anyon computers with smaller groups
• Adiabatic Preparation of Topological Order
• Quantum symmetries in discrete gauge theories
• Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory
• Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
• Ground states of quantum antiferromagnets in two dimensions
• Homological Error Correction: Classical and Quantum Codes
• Mosaic spin models with topological order
• A statistical mechanics view on Kitaev's proposal for quantum memories
• Broken quantum symmetry and confinement phases in planar physics
• Entanglement in an SU(n) Valence-Bond-Solid State
• Experimental Observation of a Topological Phase in the Maximally Entangled State of a Pair of Qubits
• Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models
• 2D Multipartite Valence Bond States in Quantum Antiferromagnets

Cited by in corpus (112)

• Condensate induced transitions between topologically ordered phases
• The Quantum Double Model with Boundary: Condensations and Symmetries
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Anyon condensation and its applications
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Introduction to topological quantum computation with non-Abelian anyons
• Diagrammatics for Bose condensation in anyon theories
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Boson Condensation in Topologically Ordered Quantum Liquids
• Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
• A hierarchy of topological tensor network states
• Twisted Fracton Models in Three Dimensions
• 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
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Simulations of quantum double models
• Topological Defect Networks for Fractons of all Types
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• An invariant of topologically ordered states under local unitary transformations
• Anyon condensation and the color code
• Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
• Excitation basis for (3+1)d topological phases
• Scaling law for topologically ordered systems at finite temperature
• Protected gates for topological quantum field theories
• Non-Abelian Hybrid Fracton Orders
• Towards a mathematical formalism for classifying phases of matter
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
• Kitaev lattice models as a Hopf algebra gauge theory
• On Defects Between Gapped Boundaries in Two-Dimensional Topological Phases of Matter
• Haag duality for Kitaev's quantum double model for abelian groups
• Interacting Anyonic Fermions in a Two-Body Color Code Model
• Efficient Machine Learning Representations of Surface Code with Boundaries, Defects, Domain Walls and Twists
• Generalized Cluster States Based on Finite Groups
• Topological Quantum Computation with Gapped Boundaries
• Kitaev's Lattice Model and Turaev-Viro TQFTs
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• On the stability of charges in infinite quantum spin systems
• The complete set of infinite volume ground states for Kitaev's abelian quantum double models
• Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy
• Generalized Toric Codes Coupled to Thermal Baths
• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Characterizing topological order by the information convex
• Seeing topological entanglement through the information convex
• Kitaev's quantum double model from a local quantum physics point of view
• From 3D topological quantum field theories to 4D models with defects
• Universal quantum computation in the surface code using non-Abelian islands
• Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras
• Exactly soluble lattice models for non-abelian states of matter in 2 dimensions
• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Symmetry reduction induced by anyon condensation: a tensor network approach
• Anyons are not energy eigenspaces of quantum double Hamiltonians
• Boundary and domain wall theories of 2d generalized quantum double model
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Finite temperature quantum simulation of stabilizer Hamiltonians
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Generalized Color Codes Supporting Non-Abelian Anyons
• Universal structure of measurement-induced information in many-body ground states
• Multipartite edge modes and tensor networks
• Jones index, secret sharing and total quantum dimension
• Quantum double aspects of surface code models
• Fracton-like phases from subsystem symmetries
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons
• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Superuniversality from disorder at two-dimensional topological phase transitions
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• From entanglement renormalisation to the disentanglement of quantum double models
• Quantum edge modes in 3d gravity and 2+1d topological phases of matter
• Simulation of non-Abelian Anyons using ribbon operators connected to a common base site
• Protocols for Creating Anyons and Defects via Gauging
• Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases
• Quantum phase transitions in the $K$-layer Ising toric code
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview
• Non-Abelian Fusion Rules from an Abelian System
• An entropic invariant for 2D gapped quantum phases
• Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Entanglement Entropy of Topological Orders with Boundaries
• A Universal Circuit Set Using the $S_3$ Quantum Double
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• A dynamical Toric Code model with fusion and de-fusion
• Electric-magnetic duality and ${\mathbb{Z}}_2$ symmetry enriched Abelian lattice gauge theory
• Topological Quantum Computation with Gapped Boundaries and Boundary Defects
• Soft symmetries of topological orders
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases III: the (3+1)-Dimensional Case
• Dynamical abelian anyons with bound states and scattering states
• Self-Correcting Quantum Computers
• Fibre bundle framework for unitary quantum fault tolerance
• Poisson-geometric analogues of Kitaev models
• Braid Group Representations from Braiding Gapped Boundaries of Dijkgraaf-Witten Theories
• Mixed-State Quantum Spin Liquids and Dynamical Anyon Condensations in Kitaev Lindbladians
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Knots and signal transmission in topological quantum devices
• Defects in Kitaev models and bicomodule algebras
• Generating domain walls between topologically ordered phases using quantum double models
• Toric code-like models from the parameter space of $3D$ lattice gauge theories
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model
• Topologically ordered states in infinite quantum spin systems
• The category of anyon sectors for non-abelian quantum double models
• Spin chains, defects, and quantum wires for the quantum-double edge
• Modified toric code models with flux attachment from Hopf algebra gauge theory
• Oriented Closed Polyhedral Maps and the Kitaev Model
• Twisted Lattice Gauge Theory: Membrane Operators, Three-loop Braiding and Topological Charge
• Knots and entanglement
• Universal Gates from Braiding and Fusing Anyons on Quantum Hardware