String-net condensation: A physical mechanism for topological phases

Abstract

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and condense. We derive exactly soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states. Those ground states correspond to 2D parity invariant topological phases. These models reveal the mathematical framework underlying topological phases: tensor category theory. One of the Hamiltonians - a spin-1/2 system on the honeycomb lattice - is a simple theoretical realization of a fault tolerant quantum computer. The higher dimensional case also yields an interesting result: we find that 3D string-net condensation naturally gives rise to both emergent gauge bosons and emergent fermions. Thus, string-net condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions.

arXiv comment21 pages, RevTeX4, 19 figures. Homepage http://dao.mit.edu/~wen

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• (3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces
• Local tensor network for strongly correlated projective states
• Spin-1 Kitaev model in one dimension
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Tensor network approach to phase transitions of a non-Abelian topological phase
• The modular S-matrix as order parameter for topological phase transitions
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• When a local Hamiltonian must be frustration-free
• Universal lower bound on topological entanglement entropy
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Simple-current algebra constructions of 2+1D topological orders
• Condensate-induced transitions and critical spin chains
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Enhancing Detection of Topological Order by Local Error Correction
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• Entanglement Spectrum as a Probe for the Topology of a Spin-Orbit Coupled Superconductor
• Intrinsic sign problems in topological quantum field theories
• Symmetry protected topological orders of 1D spin systems with D2+T symmetry
• On the stability of charges in infinite quantum spin systems
• Gapped symmetric edges of symmetry protected topological phases
• Explicit monodromy of Moore-Read wave functions on a torus
• Decoherence Patterns of Topological Qubits from Majorana Modes
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• On Enriching the Levin-Wen model with Symmetry
• Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code
• String flux mechanism for fractionalization in topologically ordered phases
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• String Condensations in 3+1D and Lagrangian Algebras
• Properties of Quantum Graphity at Low Temperature
• Focus on topological quantum computation
• Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
• Composing topological domain walls and anyon mobility
• Conservation laws and quantum error correction: towards a generalised matching decoder
• Realizing topologically ordered states on a quantum processor
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Modular transformations through sequences of topological charge projections
• Mean-field ansatz for topological phases with string tension
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• `Gauging' time reversal symmetry in tensor network states
• Quenching across quantum critical points: role of topological patterns
• Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Topological orders and factorization homology
• Robustness of Topological Order in the Toric Code with Open Boundaries
• Free-fermion descriptions of parafermion chains and string-net models
• Computing data for Levin-Wen with defects
• Toward a 3d Ising model with a weakly-coupled string theory dual
• Topological order: from long-range entangled quantum matter to an unification of light and electrons
• Reduced fidelity in Kitaev honeycomb model
• Ashkin-Teller universality in a quantum double model of Ising anyons
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Quantum phase transitions out of a Z2 x Z2 topological phase
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• Detecting Topological Order with Ribbon Operators
• Dichromatic state sum models for four-manifolds from pivotal functors
• Engineered Open Systems and Quantum Simulations with Atoms and Ions
• Effect of ring-exchange interactions in the extended Kitaev honeycomb model
• Local interactions and non-Abelian quantum loop gases
• Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• 3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators
• Walker-Wang models and axion electrodynamics
• Folding approach to topological orders enriched by mirror symmetry
• Seeing topological entanglement through the information convex
• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Characterizing topological order by the information convex
• Can long-range interactions stabilize quantum memory at nonzero temperature?
• Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders
• Topological order, entanglement, and quantum memory at finite temperature
• Emergent U(1) gauge theory with fractionalized boson/fermion from the bose condensation of exciton in multi-band insulator
• Nested Topological Order
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• A Bionic Coulomb Phase on the Pyrochlore Lattice
• Simulating topological tensor networks with Majorana qubits
• Topological quantum error correction in the Kitaev honeycomb model
• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case
• Typical Correlation Length of Sequentially Generated Tensor Network States
• Random Holographic "Large Worlds" with Emergent Dimensions
• Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
• String Phase in an Artificial Spin Ice
• Detecting topological orders through continuous quantum phase transition
• BF-theory in graphene: a route toward topological quantum computing?
• Compatible braidings with Hopf links, multi-loop, and Borromean rings in $(3+1)$-dimensional spacetime
• Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces
• Instantaneous braids and Dehn twists in topologically ordered states
• Toy model of boundary states with spurious topological entanglement entropy
• Fracton Self-Statistics
• Gapped boundaries of (3+1)d topological orders
• Emergent gauge symmetries -- making symmetry as well as breaking it
• Determination of the Semion Code Threshold using Neural Decoders
• Boson condensation and instability in the tensor network representation of string-net states
• Breakdown of Fermi liquid behavior near the hot spots in a two-dimensional model: A two-loop renormalization group analysis
• Global entanglement in a topological quantum phase transition
• Condensations in higher categories
• Exactly soluble lattice models for non-abelian states of matter in 2 dimensions
• Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras
• Topological error correcting processes from fixed-point path integrals
• Domain walls in topological phases and the Brauer-Picard ring for $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$
• Extended Coulomb liquid of paired hardcore boson model on a pyrochlore lattice
• Competing topological orders in three dimensions: X-cube versus toric code
• From 3D topological quantum field theories to 4D models with defects
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Verlinde formula from entanglement
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Quantum phase transition between symmetry enriched topological phases in tensor-network states
• Entropic Topological Invariants in Three Dimensions
• Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
• Kosaki-Longo index and classification of charges in 2D quantum spin models
• Double-semion topological order from exactly solvable quantum dimer models
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• 4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects
• On classification of modular tensor categories
• Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions
• C, P, and T of Braid Excitations in Quantum Gravity
• Josephson Coupled Moore-Read States
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• From orbifolding conformal field theories to gauging topological phases
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Modern Physics of the Condensed State: Strong Correlations and Quantum Topology
• Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta: an Elementary Method
• Emergent Braided Matter of Quantum Geometry
• Persistent Homology of ${\mathbb{Z}}_2$ Gauge Theories
• Quantum error correction with fractal topological codes
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Double semions in arbitrary dimension
• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• Holographic Software for Quantum Networks
• Unoriented 3d TFTs
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Boundary and domain wall theories of 2d generalized quantum double model
• A remark on matrix product operator algebras, anyons and subfactors
• Computing associators of endomorphism fusion categories
• Finite temperature quantum simulation of stabilizer Hamiltonians
• Exactly solvable models for U(1) symmetry-enriched topological phases
• Anyons are not energy eigenspaces of quantum double Hamiltonians
• Constructing topological models by symmetrization: A PEPS study
• Renyi entropies for classical stringnet models
• Disentangling the Generalized Double Semion Model
• Classical topological order of the Rys F-model and its breakdown in realistic spin ice: Topological sectors of Faraday loops
• Ground state entanglement constrains low-energy excitations
• On tensor network representations of the (3+1)d toric code
• Energy density of variational states
• Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
• A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter Maps
• Twisted Kitaev Bilayers and the Moiré Ising Model
• Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy
• Geodesic string condensation from symmetric tensor gauge theory: a unifying framework of holographic toy models
• Enriched string-net models and their excitations
• Systematically generated two-qubit anyon braids
• Holographic Geometries of one-dimensional gapped quantum systems from Tensor Network States
• Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits
• Symmetry protected gapless $Z_2$ spin liquids
• Invertible bimodule categories and generalized Schur orthogonality
• Symmetry-protected gapless spin liquids on the strained honeycomb lattice
• 3-Fermion topological quantum computation
• Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
• Functional completeness of planar Rydberg blockade structures
• On weak Hopf symmetry and weak Hopf quantum double model
• Generalized Color Codes Supporting Non-Abelian Anyons
• Designer non-Abelian fractons from topological layers
• Topological excitations in three dimensional Kitaev model
• No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids
• An Interferometry-Free Protocol for Demonstrating Topological Order
• Fibonacci topological order from quantum nets
• Compass and Kitaev models -- Theory and Physical Motivations
• Two-dimensional state sum models and spin structures
• Electric-Magnetic duality in twisted quantum double model of topological orders
• Quantum Current and Holographic Categorical Symmetry
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Correlation holes and slow dynamics induced by fractional statistics in gapped quantum spin liquids
• Anyonic Quantum Walks
• Effective Theory of Braid Excitations of Quantum Geometry in terms of Feynman Diagrams
• Quantifying the effect of interactions in quantum many-body systems
• Anyon condensation web and multipartite entanglement in 2D modulated gauge theories
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Criticality in Two-Dimensional Quantum Systems: Tensor Network Approach
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models
• Holographic spin networks from tensor network states
• Determining non-Abelian topological order from infinite projected entangled pair states
• Phases and phase transitions in a $U(1)\times U(1)$ system with $\theta =2\pi /3$ mutual statistics
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Fracton-like phases from subsystem symmetries
• Recoupling coefficients and quantum entropies
• Exactly Solvable Lattice Models with Crossing Symmetry
• The split and approximate split property in 2D systems: stability and absence of superselection sectors
• Multipartite edge modes and tensor networks
• Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
• Quantum thermodynamics of nonequilibrium processes in lattice gauge theories
• Non-Pauli topological stabilizer codes from twisted quantum doubles
• Vanishing Hall conductance for commuting Hamiltonians
• Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models
• Continuous error correction for Ising anyons
• Factorization Homology and 4D TQFT
• Signatures of broken parity and time-reversal symmetry in generalized string-net models
• Randomized measurement protocols for lattice gauge theories
• Wormholes and Entanglement
• 2D Quantum Double Models From a 3D Perspective
• Dual loop quantizations of 3d gravity
• Jones index, secret sharing and total quantum dimension
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• Lattice quantum codes and exotic topological phases of matter
• Constructive Simulation and Topological Design of Protocols
• Stable measurement-induced Floquet enriched topological order
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• Tensor network state correspondence and holography
• Certificates of quantum many-body properties assisted by machine learning
• Topological low-energy modes in N=0 Landau levels of graphene: a possibility of a quantum-liquid ground state
• Noise-resilient preparation of quantum many-body ground states
• (3+1)-TQFTs and Topological Insulators
• Experimental signatures of 3d fractional topological insulators
• Cusps near Topological Phase Transitions: Signatures of Majorana fermions and interactions with fluctuations
• The F-Symbols for the H3 Fusion Category
• Invertible subalgebras
• Quantum phases of a one-dimensional Majorana-Bose-Hubbard model
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Adiabatic Rotation, Quantum Search and Preparation of Superposition States
• Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants
• Renormalization group and approximate error correction
• Universality of photon counting below a bifurcation threshold
• $U_q({\mathfrak{sl}}_n)$ web models and ${\mathbb{Z}}_n$ spin interfaces
• Quantum criticality of loops with topologically constrained dynamics
• Thermalization in Kitaev's quantum double models via Tensor Network techniques
• Four revolutions in physics and the second quantum revolution -- a unification of force and matter by quantum information
• Hierarchy of Entanglement Renormalization and Long-Range Entangled States
• Topological order in interacting semimetals
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons
• Simulating 2D topological quantum phase transitions on a digital quantum computer
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
• Effective models of doped quantum ladders of non-Abelian anyons
• Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
• 2D Multipartite Valence Bond States in Quantum Antiferromagnets
• Emergent Exclusion Statistics of Fibonacci Anyons in 2D Topological Phases
• Determining topological order from infinite projected entangled pair states
• Loop condensation in the triangular lattice quantum dimer model
• Quantum computational tensor network on string-net condensate
• Russian doll spectrum in a non-Abelian string-net ladder
• Determining the structure of real-space entanglement spectrum from approximate conditional independence
• A mean field approach for string condensed states
• A unified diagrammatic approach to topological fixed point models
• Interplay between short and long-range entanglement in symmetry protected phases
• Superuniversality from disorder at two-dimensional topological phase transitions
• Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians
• CFT Correlators for Cardy Bulk Fields via String-Net Models
• Local order parameters for symmetry fractionalization
• Classical Topological Order in Abelian and Non-Abelian Generalized Height Models
• Monte Carlo study of phase transitions out of Symmetry-Enriched Topological phases of bosons in two dimensions
• Topological Minimally Entangled States via Geometric Measure
• Quantum Error-Detection at Low Energies
• Entropic topological invariant for a gapped one-dimensional system
• Sign structure and ground state properties for a spin-$S$ $t$-$J$ chain
• Locality of Edge States and Entanglement Spectrum from Strong Subadditivity
• Graph state representation of the toric code
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• A many-body Fredholm index for ground state spaces and Abelian anyons
• Entropy scaling law and the quantum marginal problem
• On symmetrization of 6j-symbols and Levin-Wen Hamiltonian
• Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks
• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• Random translation-invariant Hamiltonians and their spectral gaps
• Generalizations of Perelomov's identity on the completeness of coherent states
• Non-Abelian Anyon Superconductivity
• Composite anyon coding and the initialization of a topological quantum computer
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Decomposition in Chern-Simons theories in three dimensions
• Many-body-localization protection of eigenstate topological order in two dimensions
• Dynamical topological excitations in parafermion chains
• Spinon quantum spin Hall state in the kagome antiferromagnet with a Dzyaloshinskii-Moriya interaction
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order
• Quantum edge modes in 3d gravity and 2+1d topological phases of matter
• Classification of symmetry-enriched topological quantum spin liquids
• Wegner-Wilson loops in string nets
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• On the Entanglement Entropy of Maxwell Theory: A Condensed Matter Perspective
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Numerical simulation of non-abelian anyons
• Topological aspects of brane fields: solitons and higher-form symmetries
• Metallic states beyond Tomonaga-Luttinger liquids in one dimension
• From entanglement renormalisation to the disentanglement of quantum double models
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• On Quantum Entanglement in Topological Phases on a Torus
• A bilayer Double Semion Model with Symmetry-Enriched Topological Order
• Fragile spin liquid in three dimensions
• A New Recursion Relation for the 6j-Symbol
• Bulk-to-boundary anyon fusion from microscopic models
• Renormalization of Ising cage-net model and generalized foliation
• Tensor-product representations for string-net condensed states
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Linked Cluster Expansions via Hypergraph Decompositions
• Projector Matrix Product Operators, Anyons and Higher Relative Commutants of Subfactors
• Three-body interactions on a triangular lattice
• Crossing with the circle in Dijkgraaf-Witten theory and applications to topological phases of matter
• $U(1)$ symmetry-enriched toric code
• Probing Kitaev Models on Small Lattices
• Non-Abelian Fusion Rules from an Abelian System
• An entropic invariant for 2D gapped quantum phases
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Quantum 2-Body Hamiltonian for Topological Color Codes
• Topological and nontopological degeneracies in generalized string-net models
• Approximate symmetries of Hamiltonians
• Solvable Lattice Hamiltonians with Fractional Hall Conductivity
• Energetics of the Quantum Graphity Universe
• Bound states in string nets
• Thermal state entanglement entropy on a quantum graph
• Fusion rules and shrinking rules of topological orders in five dimensions
• Galois conjugates of String-net Model
• Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• Emergent gauge dynamics of highly frustrated magnets
• Negativity in the Generalized Valence Bond Solid State
• Towards topological fixed-point models beyond gappable boundaries
• Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction
• Quantum circuits for toric code and X-cube fracton model
• Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Quantum phase transitions in spin-1 compass chains
• Dual-isometric Projected Entangled Pair States
• Ground Subspaces of Topological Phases of Matter as Error Correcting Codes
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview
• Computing Defects Associated to Bounded Domain Wall Structures: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ Case
• Approximately-symmetric neural networks for quantum spin liquids
• Distinct-symmetry spin liquid states and phase diagram of Kitaev-Hubbard model
• The commuting local Hamiltonian on locally-expanding graphs is in NP
• Evolution of orbital angular momentum in a soft quasi-periodic structure with topological defects
• Protocols for Creating Anyons and Defects via Gauging
• Ultralocal nature of geometrogenesis
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Disentangling modular Walker-Wang models via fermionic invertible boundaries
• Robust Topological Degeneracy of Classical Theories
• Universal edge information from wave-function deformation
• Time reversal invariant gapped boundaries of the double semion state
• Playing nonlocal games with phases of quantum matter
• Topological phases of unitary dynamics: Classification in Clifford category
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Magnification of signatures of topological phase transition by quantum zero point motion
• A Universal Circuit Set Using the $S_3$ Quantum Double
• A multi-player, multi-team nonlocal game for the toric code
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case
• Towards a complete classification of non-chiral topological phases in 2D fermion systems
• Topological states in strongly correlated systems
• Topological ordering in the Majorana Toric Code
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• SU($N$) Toric Code and Nonabelian Anyons
• Ungappable edge theories with finite dimensional Hilbert spaces
• Generation of photonic tensor network states with Circuit QED
• Entangled Cloning of Stabilizer Codes and Free Fermions
• Algebraic area enumeration of random walks on the honeycomb lattice
• A dynamical Toric Code model with fusion and de-fusion
• Topologically ordered time crystals
• Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry
• Field Tensor Network States
• An anyon model in a toric honeycomb lattice
• From effective Hamiltonian to anomaly inflow in topological orders with boundaries
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians
• Boundary topological entanglement entropy in two and three dimensions
• Programming higher-order interactions of Rydberg atoms
• Hagedorn transition and topological entanglement entropy
• Classification of Metaplectic Fusion Categories
• Electric-magnetic duality and ${\mathbb{Z}}_2$ symmetry enriched Abelian lattice gauge theory
• Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• G-Extensions of Quantum Group Categories and Functorial SPT
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States
• Hubbard bands, Mott transition and deconfinement in strongly correlated systems
• Detecting topological order from modular transformations of ground states on the torus
• Entanglement in topological systems
• Bicolor loop models and their long range entanglement
• Quantum cellular automata and categorical dualities of spin chains
• Classical and quantum spin liquids
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• A Recipe for Constructing Frustration-Free Hamiltonians with Gauge and Matter Fields in One and Two Dimensions
• A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules
• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries
• Conformal geometry from entanglement
• The low-energy TQFT of the generalized double semion model
• Ising versus $SU(2{)}_2$ string-net ladder
• Entanglement subvolume law for 2D frustration-free spin systems
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Novel quantum phases on graphs using abelian gauge theory
• Dynamical generalization of Yetter's model based on a crossed module of discrete groups
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• A note on electromagnetic edge modes
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• Volume and Topological Invariants of Quantum Many-body Systems
• Classification of the phases of 1D spin chains with commuting Hamiltonians
• Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories
• $Z_3$ topological order in the quantum dimer-pentamer model
• Refined Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase
• Emergence: Key physical issues for deeper philosophical inquiries
• Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis
• Methodology for bus layout for topological quantum error correcting codes
• The Symmetry Enriched Center Functor is Fully Faithful
• Algebraic structures in two-dimensional conformal field theory
• Models of interacting bosons with exact ground states: a unified approach
• Finite-temperature properties of string-net models
• Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• Fibre bundle framework for unitary quantum fault tolerance
• Poisson-geometric analogues of Kitaev models
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• String-nets, single and double-stranded quantum loop gases for non-Abelian anyons
• The $F$-Symbols for Transparent Haagerup-Izumi Categories with $G={\mathbb{Z}}_{2n+1}$
• Dihedral twist liquid models from emergent Majorana fermions
• Generalized topological state-sum constructions and their universality
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
• Topological Quantum Computation with Gapped Boundaries and Boundary Defects
• Towards unambiguous calculation of the topological entropy for mixed states
• Fractional domain wall statistics in spin chains with anomalous symmetries
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases III: the (3+1)-Dimensional Case
• Strings in strongly correlated electron systems
• Entanglement renormalization for chiral topological phases
• Dynamical abelian anyons with bound states and scattering states
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Weak Hopf tube algebra for domain walls between 2d gapped phases of Turaev-Viro TQFTs
• Deformed quantum double realization of the toric code and beyond
• Tube Category, Tensor Renormalization and Topological Holography
• Computing the graph-changing dynamics of loop quantum gravity
• Generalized Statistics on Lattices
• Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier
• Quantum control without quantum states
• Multipartite Entanglement Structure of Fibered Link States
• Diagrammatics, Pentagon Equations, and Hexagon Equations of Topological Orders with Loop- and Membrane-like Excitations
• Topological order in symmetric blockade structures
• Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Magic Boundaries of 3D Color Codes
• Geometric properties of loop condensed phases on the square lattice
• Merging Quantum Loop Gases: a Route to Non-Abelian Topological Phases
• Local topological order and boundary algebras
• Lattice models from CFT on surfaces with holes I: Torus partition function via two lattice cells
• A witness for topological order and stable quantum memories in abelian anyonic systems
• Multi-flavor string-net models
• Geometric and computational aspects of chiral topological quantum matter
• Foundations and Applications of Entanglement Renormalization
• A characterization of a finite-dimensional commuting square producing a subfactor of finite depth
• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation
• Collective states of interacting $D(D_3)$ non-Abelian anyons
• A relation between chiral central charge and ground state degeneracy in 2+1-dimensional topological orders
• Trotter errors in digital adiabatic quantum simulation of quantum ${\mathbb{Z}}_2$ lattice gauge theory
• Coulombic antiferromagnet in spin-1/2 pyrochlores with dipole-octupole doublets
• Reflection Positivity and Levin-Wen Models
• Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases
• Emergent Kalb-Ramond fields from a dimer model
• Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions
• The ${\mathbb{Z}}_2$ toric-code and the double-semion topological order of hardcore Bose-Hubbard-type models in the strong-interaction limit
• Topological Phase Transitions Induced by Varying Topology and Boundaries in the Toric Code
• Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach
• Numerical identification and gapped boundaries of abelian fermionic topological order
• Quantum Lego and XP Stabilizer Codes
• Partially topological phase in a quantum loop gas model with tension and pressure
• Ground state degeneracy of the Ising cage-net model
• Counterexamples in Levin-Wen string-net models, group categories, and Turaev unimodality
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Representing arbitrary ground states of toric code by a restricted Boltzmann machine
• Topological Phases: An Expedition off Lattice
• Classification of Gapped Domain Walls of Topological Orders in 2+1 dimensions: A Levin-Wen Model Realization
• Condensation Completion and Defects in 2+1D Topological Orders
• Anomalies of global symmetries on the lattice
• Classification of the anyon sectors of Kitaev's quantum double model
• Permutation actions on modular tensor categories of topological multilayer phases
• Immersed figure-8 annuli and anyons
• Extended string-net models with all anyons at finite temperature
• Parent Lindbladians for Matrix Product Density Operators
• Superconductivity in a system of interacting spinful semions
• Quasi-local Frustration-Free Free Fermions
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• Preparing topologically ordered states by Hamiltonian interpolation
• Generating domain walls between topologically ordered phases using quantum double models
• Categorical Center of Higher Genera and 4D Factorization Homology
• Topological phases of the compass ladder model
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems
• Variational methods for characterizing matrix product operator symmetries
• Simplicity condition and boundary-bulk duality
• Toric code-like models from the parameter space of $3D$ lattice gauge theories
• Les Houches Lecture Notes on Tensor Networks
• Superactivation of Bell nonlocality in pure anyonic states
• Quantum field theoretic representation of Wilson surfaces: II higher topological coadjoint orbit model
• Chiral Edge States Emerging on Anyon-Net
• Abelian Topological Order on Lattice Enriched with Electromagnetic Background
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization
• Simplifying quantum double Hamiltonians using perturbative gadgets
• Entropic destruction of heavy quarkonium with hyperscaling violation
• Spin chains, defects, and quantum wires for the quantum-double edge
• Evidence for a string-net matter
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Linear-optical generation of eigenstates of the two-site XY model
• Rényi-like entanglement probe of the chiral central charge
• Simulating Topological Order on Quantum Processors
• Entropic order parameters and topological holography
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Sampling and the complexity of nature
• Emergent fracton strings from covariant bi-form gauge field theory
• Knots and entanglement
• Loops in 4+1d Topological Phases
• Three-dimensional spin-orbital liquids
• Exactly Solvable Topological Phase Transition in a Quantum Dimer Model
• Universal fault tolerant quantum computation in 2D without getting tied in knots
• Unveiling topological order through multipartite entanglement
• Symmetry-Protected Topological relationship between $SU(3)$ and $SU(2)\times U(1)$ in Two Dimension
• On a C*-Diagonal Generated by the Toric Code
• Topological Properties and Characterizations
• Phase structure of the one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory with second nearest-neighbor interactions
• Categorical Quantum Volume Operator
• Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
• Entanglement transition and suppression of critical phase of thermofield double state in monitored quantum circuit with unitary $R$ matrix gates
• The topological order of the space
• Work and heat exchanged during sudden quenches of strongly coupled quantum systems
• Skeleton of isometric Tensor Network States for Abelian String-Net Models
• A Mathematical Picture Language Project
• The Gauge Picture of Quantum Dynamics
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
• |Z_{Kup}|=|Z_{Henn}|^2 for Lens spaces
• From categories to anyons: a travelogue
• Note on searching for critical lattice models as entropy critical points from strange correlator
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries
• Free fermion representation of the topological surface code
• Z${}_2$ topological orders in kagomé dipolar systems: Feedback from Rydberg quantum simulator
• Condensation of non-Abelian $SU(3{)}_{N_f}$ anyons in a one-dimensional fermion model
• Tensor network states for the description of quantum many-body systems
• Twisted quantum doubles are sign problem-free
• Topological phase diagram of $\mathcal{D}(S_3)$ induced by forbidding charges and fluxes
• Partition function of the Kitaev quantum double model
• Boson-Lattice Construction for Anyon Models
• Topological order on the Bloch sphere
• Exact Mappings in Condensed Matter Physics
• «Anticommuting» ${\mathbb{Z}}_2$ quantum spin liquids
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling
• Emergent Symmetry and Phase Transitions on the Domain Wall of ${\mathbb{Z}}_2$ Topological Orders
• Network topology transition at criticality
• Twisted Lattice Gauge Theory: Membrane Operators, Three-loop Braiding and Topological Charge
• Symmetry-protected topological corner modes in a periodically driven interacting spin lattice
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions
• Semidual Kitaev lattice model and tensor network representation
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly
• Combinatorics and algebra of tensor calculus
• Topology-driven phase transitions in the classical monomer-dimer-loop model
• Topological approach toward quantum codes with realistic physical constraints
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization
• A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects
• Hidden subsystem symmetry protected states in competing topological orders
• Emergent Symmetry-Protected Topological Phases via Polyakov Confinement in Quantum Spin Systems
• Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States