Anyons in an exactly solved model and beyond

2005/06/17 by Alexei Kitaev · 2 voices · 5,371 citations
Physics and Astronomy · #Abelian group #Fermion #Gauge theory #Ising model #Mathematical physics #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological quantum computer #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1016/j.aop.2005.10.005

published in Annals of Physics 321(1), 2-111 (Elsevier BV) · 113 pages. LaTeX + 299 .eps files (see comments in hexagon.tex for known-good compilation environment). VERSION 3: some typos fixed, one reference added

arxiv published 2005/06/17 · openalex publication_date 2006/01/01 · arxiv created 2008/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static ℤ₂ gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and non-Abelian phases of the original model correspond to ν=0 and ν=± 1, respectively. The anyonic properties of excitation depend on ν\bmod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.

Citations

• Fault-tolerant quantum computation by anyons

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• Double-semion topological order from exactly solvable quantum dimer models
• Generalizations and limitations of string-net models
• Quantum simulation and ground state preparation for the honeycomb Kitaev model
• Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice
• Topological order from quantum loops and nets
• Exotic phase diagram of a topological quantum system
• Manipulating unpaired Majorana fermions in a quantum spin chain
• Kitaev model and dimer coverings on the honeycomb lattice
• Benchmarking the Planar Honeycomb Code
• TopologicalπJosephson junction in superconducting Rashba wires
• Bosonic Mott Insulator with Meissner Currents
• Schrieffer–Wolff transformation for quantum many-body systems
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Geometry defects in bosonic symmetry-protected topological phases
• Dynamics of a quantum phase transition and relaxation to a steady state
• Exotic superconductivity in the doped Kitaev quantum spin liquid
• Quantum information theory and Fourier multipliers on quantum groups
• Genetic braid optimization: A heuristic approach to compute quasiparticle braids
• Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states
• One-dimensional itinerant interacting non-Abelian anyons
• Entanglement and Majorana edge states in the Kitaev model
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Topological Degeneracy and Vortex Manipulation in Kitaev’s Honeycomb Model
• Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line
• A family of stabilizer codes for D(ℤ₂) anyons and Majorana modes
• Constraints on Topological Order in Mott Insulators
• Information-theoretical formulation of anyonic entanglement
• Composite Dirac Liquids: Parent States for Symmetric Surface Topological Order
• Short-Range Correlations in the Magnetic Ground State ofNa4Ir3O8
• Long-range interactions in the effective low-energy Hamiltonian of Sr2IrO4: A core-to-core resonant inelastic x-ray scattering study
• Particle-Hole Duality in the Lowest Landau Level
• Fermions and nontrivial loop-braiding in a three-dimensional toric code
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Layer Construction of 3D Topological States and String Braiding Statistics
• Crystal electric field excitations in the quantum spin liquid candidate NaErS2
• Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling
• Vaporization of Kitaev Spin Liquids
• Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
• E8 Spectra of Quasi-One-Dimensional Antiferromagnet BaCo2V2O8 under Transverse Field
• Kitaev-Heisenberg-J2-J3model for the iridatesA2IrO<mml:mrow/>3
• Non-abelian Quantum Statistics on Graphs
• Magnetic-Field-Driven Dimensional Reduction in a Quantum Antiferromagnet
• Role of quantum fluctuations on spin liquids and ordered phases in the Heisenberg model on the honeycomb lattice
• Semiclassical ground-state phase diagram andmulti-Qphase of a spin-orbit-coupled model on triangular lattice
• Diagnosing phases of magnetic insulators via noise magnetometry with spin qubits
• Position-momentum duality in the entanglement spectrum of free fermions
• Topological bootstrap: Fractionalization from Kondo coupling
• Some non-braided fusion categories of rank 3
• Quantum critical phase transition between two topologically ordered phases in the Ising toric code bilayer
• Topological magnons in ferromagnetic Kitaev-Heisenberg model on CaVO lattice
• Jeff=1/2 Hyperoctagon Lattice in Cobalt Oxalate Metal-Organic Framework
• Magnetic Properties of Restacked 2D Spin 1/2 honeycomb RuCl3 Nanosheets
• Spin–Orbit-Entangled Electronic Phases in 4d and 5d Transition-Metal Compounds
• Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach
• Finite-temperature phase transition to a Kitaev spin liquid phase on a hyperoctagon lattice: A large-scale quantum Monte Carlo study
• Synthetic charge-flux quantum liquids
• Fault-tolerant holonomic quantum computation in surface codes
• Anomaly constraint on chiral central charge of (2+1)d topological order
• Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare-earth pyrochlore magnets: A fermionic parton approach
• Theory of twist liquids: Gauging an anyonic symmetry
• Hidden Anderson localization in disorder-free Ising–Kondo lattice*
• Projective symmetry group analysis of inelastic light scattering in Kitaev spin balls
• Fault-tolerant quantum gates with defects in topological stabilizer codes
• Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Competing topological orders in three dimensions: X-cube versus toric code
• Exact diagonalization study of the anisotropic Heisenberg model related to YbMgGaO4
• Comments on one-form global symmetries and their gauging in 3d and 4d
• Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits
• Adiabatic dynamics in passage across quantum critical lines and gapless phases
• From entanglement renormalisation to the disentanglement of quantum double models
• Multi-qudit states generated by unitary braid quantum gates based on Temperley-Lieb algebra
• Free parafermions
• Universal thermodynamics in the Kitaev fractional liquid
• Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl3
• Exact solution of theD3non-Abelian anyon chain
• An Invariant of Topologically Ordered States Under Local Unitary Transformations
• Localization and delocalization of fermions in a background of correlated spins
• Linear and nonlinear optical responses in Kitaev spin liquids
• Energetic cost of Hamiltonian quantum gates
• The \bfZ_\bf2 toric-code and the double-semion topological order of hardcore Bose-Hubbard-type models in the strong-interaction limit
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Braiding Non-Abelian Quasiholes in Fractional Quantum Hall States
• Simulating Exotic Phases of Matter with Bond-Directed Interactions with Arrays of Majorana-Cooper Pair Boxes
• Observation of Coexisting Weak Localization and Superconducting Fluctuations in Strained Sn1–xInxTe Thin Films
• Anomalous matrix product operator symmetries and 1D mixed-state phases
• Fermionization of bosons in a flat band
• Anisotropic layer construction of anisotropic fracton models
• Gapfull and gapless 1D Topological Superconductivity in Spin-Orbit Coupled Bilayer Graphene
• Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
• Exotic topological types of Majorana zero modes and their universal quantum manipulation
• Q-colourings of the triangular lattice: exact exponents and conformal field theory
• Spin-(1)/(2) kagome Heisenberg antiferromagnet with strong breathing anisotropy
• Criticality and magnetic phases of Ising Shastry-Sutherland candidate holmium tetraboride
• KOMPASS: the new cold neutron triple-axis-spectrometer specialized for polarization analysis
• Reduced fidelity in the Kitaev honeycomb model
• Direct measurement of Bacon-Shor code stabilizers
• Destabilization of Magnetic Order in a Dilute Kitaev Spin Liquid Candidate
• Ultralow-Temperature Thermal Conductivity of the Kitaev Honeycomb Magnet α−RuCl3 across the Field-Induced Phase Transition
• The enigma of theν=2+3/8fractional quantum Hall effect
• Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
• Prethermal Strong Zero Modes and Topological Qubits
• Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for α−RuCl3 and Na2IrO3
• Exactly solvable model of topological insulator realized on spin- \tfrac12 lattice
• Divergent Thermopower without a Quantum Phase Transition
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Highly anisotropic exchange interactions ofjeff=12iridium moments on the fcc lattice inLa2BIrO6 (B=Mg,<mml:mspace width="0.16em"/>Zn)
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Spin-one bilinear-biquadratic model on a star lattice
• Strain- and pressure-tuned magnetic interactions in honeycomb Kitaev materials
• Experimental realization of classical Z2 spin liquids in a programmable quantum device
• One dimensional gapped quantum phases and enriched fusion categories
• Sachdev-Ye-Kitaev type physics in the strained Kitaev honeycomb model
• Finite-temperature phase transition to a quantum spin liquid in a three-dimensional Kitaev model on a hyperhoneycomb lattice
• Revealing frustrated local moment model for pressurized hyperhoneycomb iridate: Paving the way toward a quantum spin liquid
• Fault-tolerant gates via homological product codes
• Dynamical quantum phase transitions in the Kitaev honeycomb model
• SU(N)magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• Coherence susceptibility as a probe of quantum phase transitions
• Vacancy-Induced Low-Energy Density of States in the Kitaev Spin Liquid
• Pressure-induced melting of magnetic order and emergence of a new quantum state in α−RuCl3
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
• Low-temperature crystal and magnetic structure ofα−RuCl3
• Spin networks and anyonic topological computing
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Quantum computation with Turaev–Viro codes
• Mapping Kitaev’s quantum double lattice models to Levin and Wen’s string-net models
• Rigorous calculations of non-Abelian statistics in the Kitaev honeycomb model
• Frustrated Quantum Rare-Earth Pyrochlores
• Variational study of the Kitaev-Heisenberg-Gamma model
• Chiral bosonic topological insulator on the honeycomb lattice with anisotropic interactions
• Thermally induced metallic phase in a gapped quantum spin liquid: Monte Carlo study of the Kitaev model with parity projection
• Symmetry fractionalization in the topological phase of the spin-12J1−J2triangular Heisenberg model
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Effects of spin vacancies on magnetic properties of the Kitaev-Heisenberg model
• Entanglement dualities in supersymmetry
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Braiding defects in topological stabiliser codes of any dimension cannot\n be universal
• Absence of Fibonacci anyons in Rydberg chains
• Time-reversal-invariant C2-symmetric higher-order topological superconductors
• Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO3
• Monte Carlo simulation of equilibrium and dynamic phase transition properties of an Ising bilayer
• Z3 topological order in the quantum dimer-pentamer model
• Interplay between Kitaev interaction and single ion anisotropy in ferromagnetic CrI3 and CrGeTe3 monolayers
• Diagnosing Topological Edge States via Entanglement Monogamy
• Crystalline electric field excitations in the quantum spin liquid candidate NaYbSe2
• Mechanism of the insulator-to-metal transition and superconductivity in the spin liquid candidate NaYbSe2 under pressure
• Exactly solvable models of spin liquids with spinons, and of three-dimensional topological paramagnets
• Chiral topological superconductivity in Josephson junctions
• Chiral Floquet Phases of Many-Body Localized Bosons
• Optical engineering and detection of magnetism in moiré semiconductors
• Majorana modes and p-wave superfluids for fermionic atoms in optical lattices
• Entangled cloning of stabilizer codes and free fermions
• Exactly solvable 2D topological Kondo lattice model
• Chemistry of Quantum Spin Liquids
• Anisotropic superexchange through nonmagnetic anions with spin-orbit coupling
• Bulk-Boundary Correspondence for Three-Dimensional Symmetry-Protected Topological Phases
• Random translation-invariant Hamiltonians and their spectral gaps
• Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment
• Anomaly indicators and bulk-boundary correspondences for three-dimensional interacting topological crystalline phases with mirror and continuous symmetries
• Strategy to extract Kitaev interaction using symmetry in honeycomb Mott insulators
• Qudit hypergraph states
• Floquet engineering of Mott insulators with strong spin-orbit coupling
• Braiding statistics and congruent invariance of twist defects in bosonic bilayer fractional quantum Hall states
• Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction
• Twisted Boundary Condition and Lieb-Schultz-Mattis Ingappability for Discrete Symmetries
• Local probes for charge-neutral edge states in two-dimensional quantum magnets
• Spin wave theory of a one-dimensional generalized Kitaev model
• Como achei a fazenda da senadora golpista Ana Amélia
• Experimental simulation of anyonic fractional statistics with an NMR quantum-information processor
• Coupled spin-12 ladders as microscopic models for non-Abelian chiral spin liquids
• Measurement-protected quantum phases
• Dynamic creation of a topologically-ordered Hamiltonian using spin-pulse control in the Heisenberg model
• Quantum spin liquid states
• Thermal Transport in the Kitaev Model
• Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code
• Fractional Spin Fluctuations as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
• Kitaev honeycomb and other exotic spin models with polar molecules
• Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions
• Distinct-symmetry spin-liquid states and phase diagram of the Kitaev-Hubbard model
• Pairing Obstructions in Topological Superconductors
• Universal fault-tolerant measurement-based quantum computation
• Tensor network state approach to quantum topological phase transitions and their criticalities of Z2 topologically ordered states
• Exact chiral spin liquid with stable spin Fermi surface on the kagome lattice
• Quantum anomalous Hall Majorana platform
• Fractional Quantum Hall Effects
• Equivalence of topological insulators and superconductors
• Integrability and Braided Tensor Categories
• High-pressure magnetization and NMR studies of α−RuCl3
• Choreographed entanglement dances: Topological states of quantum matter
• Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits
• Probing quantum spin liquids in equilibrium using the inverse spin Hall effect
• Physical solutions of the Kitaev honeycomb model
• Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid
• Thermal and magnetoelastic properties of α-RuCl 3 in the field-induced low temperature states
• Majorana representation for dissipative spin systems
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material α-RuCl₃
• Topologically protected quantum state transfer in a chiral spin liquid
• Uranium in its natural compounds
• Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid
• Anyonic Chains, Topological Defects, and Conformal Field Theory
• Kitaev-Heisenberg Hamiltonian for high-spin d7 Mott insulators
• Theory of the field-revealed Kitaev spin liquid
• On the stability of topological phases on a lattice
• The (2 + 1)-d U(1) quantum link model masquerading as deconfined criticality
• Detecting topological order with ribbon operators
• Twofold twist defect chains at criticality
• Kmatrix construction of symmetry-enriched phases of matter
• Proximate Kitaev system for an intermediate magnetic phase in in-plane magnetic fields
• Majorana Fermions and Topology in Superconductors
• Topological quantum computation based on chiral Majorana fermions
• Quantum phase transition in Heisenberg-Kitaev model
• Spin-12 Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks
• Chemical and hydrostatic-pressure effects on the Kitaev honeycomb material Na2IrO3
• Ising anyons in frustration-free Majorana-dimer models
• Non-Abelian statistics of vortices with non-Abelian Dirac fermions
• Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State
• Incommensurate counterrotating magnetic order stabilized by Kitaev interactions in the layered honeycombα−Li2IrO3
• Tensor network wave function of S=1 Kitaev spin liquids
• Flux mobility delocalization in the Kitaev spin ladder
• Edge states and topological orders in the spin liquid phases of star lattice
• Symmetry-protected non-Fermi liquids, kagome spin liquids, and the chiral Kondo lattice model
• Excitations in the field-induced quantum spin liquid state of α-RuCl3
• Properties and application of SO(3) Majorana representation of spin: Equivalence with Jordan-Wigner transformation and exact Z2 gauge theories for spin models
• Quantized charge transport in chiral Majorana edge modes
• Vacancies in Kitaev quantum spin liquids on the three-dimensional hyperhoneycomb lattice
• Mixed states from anomalies
• Simulating spin systems with Majorana networks
• Gapless spin liquids in disguise
• Critical theory of the topological quantum phase transition in anS=2spin chain
• Lattice dynamics and structural transition of the hyperhoneycomb iridate β−Li2IrO3 investigated by high-pressure Raman scattering
• Thermal conductivity of local moment models with strong spin-orbit coupling
• Local Raman spectroscopy of chiral Majorana edge modes in Kitaev spin liquids and topological superconductors
• Universal nonanalytic behavior of the Hall conductance in a Chern insulator at the topologically driven nonequilibrium phase transition
• Competing spin-liquid states in the spin-12Heisenberg model on the triangular lattice
• Some experimental schemes to identify quantum spin liquids*
• Spin-SKitaev model: Classical ground states, order from disorder, and exact correlation functions
• Thermal canting of spin-bond order
• Jsymm: A Python package for symmetry analysis of exchange tensors in magnetic Hamiltonians
• Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state
• Nonlocal nonstabilizerness for slightly entangled quantum many-body states
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field
• Intermediate phases in α-RuCl₃ under in-plane magnetic field via interlayer spin interactions
• Classification of Interacting Topological Floquet Phases in One Dimension
• Quantum lattice model solver HΦ
• Possible interaction-driven topological phases in (111) bilayers of LaNiO<mml:mrow/>3
• Doped Mott Insulators in (111) Bilayers of Perovskite Transition-Metal Oxides with a Strong Spin-Orbit Coupling
• Fractional topological phase in one-dimensional flat bands with nontrivial topology
• Spin-Orbital Intertwined Topological Superconductivity in a Class of Correlated Noncentrosymmetric Materials
• Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement
• Variational principle for the time evolution operator, its usefulness in effective theories of condensed matter systems and a glimpse into the role played by the quantum geometry of unitary transformations
• Endstates in multichannel spinlessp-wave superconducting wires
• Protected gates for topological quantum field theories
• Planar quantum low-density parity-check codes with open boundaries
• Emergent phases in the Yao-Lee model via coupling to topological spin textures
• Holographic duality from Howe duality: Chern-Simons gravity as an ensemble of code CFTs
• Clifford algebras and liquid crystalline fermions
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems
• Interpreting machine learning of topological quantum phase transitions
• Possible phases of the spin-12 XXZ model on a honeycomb lattice by boson-vortex duality
• Intertwining Josephson and Vortex Topologies in Conventional Superconductors
• Tunneling Spectroscopy of Quantum Spin Liquids
• Barrier tunneling of the loop-nodal semimetal in the hyperhoneycomb lattice
• Spin dynamics of the planar kagome lattice ferromagnet with four-site ring exchange processes
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Fractional quantum Hall effect in optical lattices
• Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit
• Magnetic order inα−RuCl3: A honeycomb-lattice quantum magnet with strong spin-orbit coupling
• AnisotropicRu3+ 4d5magnetism in theα−RuCl3honeycomb system: Susceptibility, specific heat, and zero-field NMR
• Spin-Wave Excitations Evidencing the Kitaev Interaction in Single Crystalline α−RuCl3
• Local nuclear and magnetic order in the two-dimensional spin glass Mn0.5Fe0.5PS3
• High-field quantum disordered state in α−RuCl3: Spin flips, bound states, and multiparticle continuum
• Excitonic magnetism at the intersection of spin-orbit coupling and crystal-field splitting
• Breakdown of magnons in a strongly spin-orbital coupled magnet. [europepmc]
• Quantum spin liquid in the semiclassical regime. [europepmc]
• Experimental demonstration of angular momentum-dependent topological transport using a transmission line network. [europepmc]
• Theory of the field-revealed Kitaev spin liquid. [europepmc]
• Nonreciprocal charge transport at topological insulator/superconductor interface. [europepmc]
• Non-Hermitian fractional quantum Hall states. [europepmc]
• Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnet α-RuCl 3 . [europepmc]
• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets. [europepmc]
• Photonic Floquet topological insulators in a fractal lattice. [europepmc]
• Spin Hamiltonians in Magnets: Theories and Computations. [europepmc]
• Order-by-disorder from bond-dependent exchange and intensity signature of nodal quasiparticles in a honeycomb cobaltate. [europepmc]
• Robust spin correlations at high magnetic fields in the harmonic honeycomb iridates. [europepmc]
• Proximate ferromagnetic state in the Kitaev model material α-RuCl 3 . [europepmc]
• Mixed alkali-ion transport and storage in atomic-disordered honeycomb layered NaKNi 2 TeO 6 . [europepmc]
• Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na 2 Co 2 TeO 6 . [europepmc]
• Topological phases of quantized light. [europepmc]
• The Magnetic Genome of Two-Dimensional van der Waals Materials. [europepmc]
• Observation of novel topological states in hyperbolic lattices. [europepmc]
• Classification of time-reversal-invariant crystals with gauge structures. [europepmc]
• Non-Abelian braiding of graph vertices in a superconducting processor. [europepmc]
• Spin-resolved topology and partial axion angles in three-dimensional insulators. [europepmc]
• Spin-orbit entanglement driven by the Jahn-Teller effect. [europepmc]
• Particle exchange statistics beyond fermions and bosons. [europepmc]
• Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl 3 . [europepmc]
• Correlated states in β-Li 2 IrO 3 driven by applied magnetic fields. [europepmc]

Discussions

• An important open mathematical problem in the theoretical foundation of topological order is to prove that the universal properties (braiding and fusion) of point-like excitations in any gapped phase [stackexchange, 3 points]
• You're hitting on a very interesting general feature of our state of understanding of topological quantum order. Given any "doubled" TQFT, we can construct a physical system on the lattice whose low e [stackexchange, 1 points]