Exact results for spin dynamics and fractionization in the Kitaev Model

Abstract

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in non-trivial quantum spin models. The result is also novel: in spite of presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation, showing existence of a gapless but short range spin liquid. An unusual, \emph{all energy scale fractionization}of a spin -flip quanta, into two infinitely massive $\pi$-fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.

arXiv comment4 pages, 2 figures. Typose corrected, figure made better, clarifying statements and references added

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Cited by in corpus (297)

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• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
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• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• An exact chiral spin liquid with non-Abelian anyons
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• Fermionic response from fractionalization in an insulating two-dimensional magnet
• Breakdown of Magnons in a Strongly Spin-Orbital Coupled Magnet
• Hunting Majorana Fermions in Kitaev Magnets
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Gapless Spin Excitations in the Field-Induced Quantum Spin Liquid Phase of alpha-RuCl3
• Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Vaporization of Kitaev spin liquids
• Anomalous thermal conductivity and magnetic torque response in the honeycomb magnet $\alpha$-RuCl${}_3$
• Finite-temperature phase diagram of the Heisenberg-Kitaev model
• Exactly solvable Kitaev model in three dimensions
• Large field-induced gap of Kitaev-Heisenberg paramagnons in $\alpha$-RuCl${}_3$
• Exact results for quench dynamics and defect production in a two-dimensional model
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Raman Scattering Signatures of Kitaev Spin Liquids in A${}_2$ IrO${}_3$ Iridates
• Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2
• Dynamics of Fractionalization in Quantum Spin Liquids
• Microscopic mechanism for higher-spin Kitaev model
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Observation of two types of anyons in the Kitaev honeycomb magnet
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Relation between Kitaev magnetism and structure in $\alpha$-RuCl${}_3$
• Quantum spin liquid signatures in Kitaev-like frustrated magnets
• Topological phases, Majorana modes and quench dynamics in a spin ladder system
• Low-energy Spin Dynamics of the Honeycomb Spin Liquid Beyond the Kitaev Limit
• Algebraic spin liquid in an exactly solvable spin model
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Fractional Spin Fluctuation as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates $\beta$- and $\gamma$-Li${}_2$IrO${}_3$
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Antiferromagnetic resonance and terahertz continuum in $\alpha -$RuCl${}_3$
• Quantum Phase Transition in Heisenberg-Kitaev Model
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
• Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: the $J_1$--$J_2$--$J_3$ model
• Site dilution in Kitaev's honeycomb model
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Honeycomb Layered Oxides: Structure, Energy Storage, Transport, Topology and Relevant Insights
• Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
• Witnessing quantum criticality and entanglement in the triangular antiferromagnet KYbSe${}_2$
• Witnessing entanglement in quantum magnets using neutron scattering
• Emergent Fermions and Anyons in the Kitaev Model
• Large Thermal Hall Effect in $\alpha$-RuCl${}_3$: Evidence for Heat Transport by Kitaev-Heisenberg Paramagnons
• Proximate ferromagnetic state in the Kitaev model material $\alpha$-RuCl${}_3$
• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• Ultralow-temperature thermal conductivity of the Kitaev honeycomb magnet $\alpha$-RuCl${}_3$ across the field-induced phase transition
• Physical solutions of the Kitaev honeycomb model
• Unconventional spin dynamics in the honeycomb-lattice material $\alpha$-RuCl${}_3$: high-field ESR studies
• Local Probes for Charge-Neutral Edge States in Two-Dimensional Quantum Magnets
• A $\Gamma$-matrix generalization of the Kitaev model
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• Dynamical Localization in ${\mathbb{Z}}_2$ Lattice Gauge Theories
• Magnetic thermal conductivity far above the Néel temperatures in the Kitaev-magnet candidate $\alpha$-RuCl${}_3$
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Majorana edge modes in the Kitaev model
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Creation and Manipulation of Anyons in the Kitaev Model
• Successive Majorana Topological Transitions Driven by a Magnetic Field in the Kitaev Model
• Tunneling spectroscopy of quantum spin liquids
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• Diagnosing phases of magnetic insulators via noise magnetometry with spin qubits
• Resonant inelastic X-ray scattering response of the Kitaev honeycomb model
• Exotic low-energy excitations emergent in the random Kitaev magnet Cu${}_2$IrO${}_3$
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
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• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
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• Pressure-induced melting of magnetic order and emergence of new quantum state in alpha-RuCl3
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• Topological spinon semimetals and gapless boundary states in three dimensions
• Electrical Access to Ising Anyons in Kitaev Spin Liquids
• Dynamics of visons and thermal Hall effect in perturbed Kitaev models
• Intermediate gapless phase and topological phase transition of Kitaev model in a uniform magnetic field
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Variational study of the Kitaev-Heisenberg-Gamma model
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• Electronic and phonon excitations in α-RuCl${}_3$
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• Kitaev honeycomb models in magnetic fields: Dynamical response and hidden symmetries
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• Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
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• Jahn-Teller effect in systems with strong on-site spin-orbit coupling
• Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
• Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings
• Tunneling spectroscopy as a probe of fractionalization in 2D magnetic heterostructures
• Driven quantum many-body systems and out-of-equilibrium topology
• Ground-state phases of the frustrated spin-1/2 $J_1$--$J_2$--$J_3$ Heisenberg ferromagnet ($J_1<0$) on the honeycomb lattice with $J_3=J_2>0$
• Interlayer Coupling Effect on a Bilayer Kitaev Model
• Exact treatment of magnetism-driven ferroelectricity in the one-dimensional compass model
• Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$\Gamma$ chain
• Scanning tunneling spectroscopy of Majorana zero modes in a Kitaev spin liquid
• An exactly solvable BCS-Hubbard Model in arbitrary dimensions
• Hidden Quasiparticles and Incoherent Photoemission Spectra in Na2IrO3
• Spin correlations and phase diagram of the perturbed Kitaev model
• Quantum spin liquid ground states of the Heisenberg-Kitaev model on the triangular lattice
• Universal Thermodynamics in the Kitaev Fractional Liquid
• Complete phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ model (with $J_3=J_2$) on the honeycomb lattice
• Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin structure factor, magnetic susceptibility, and NMR relaxation rate
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• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
• Putative spin liquid in the triangle-based iridate Ba${}_3$IrTi${}_2$O${}_9$
• High-field thermal transport properties of the Kitaev quantum magnet alpha-RuCl3: evidence for low-energy excitations beyond the critical field
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• Majorana-Magnon Crossover by a Magnetic Field in the Kitaev Model: Continuous-Time Quantum Monte Carlo Study
• Quantum information approach to the quantum phase transition in the Kitaev honeycomb model
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• Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids
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• Majorana spectroscopy of 3D Kitaev spin-liquids
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• Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models
• Finite-temperature phase transition to a Kitaev spin liquid phase on a hyperoctagon lattice: A large-scale quantum Monte Carlo study
• Determining Kitaev interaction in spin-$S$ honeycomb Mott insulators
• Quenching across quantum critical points: role of topological patterns
• Spin-Liquid--to--Spin-Liquid Transition in Kitaev Magnets Driven by Fractionalization
• Scattering Signatures of Bond-Dependent Magnetic Interactions
• Unquantized thermal Hall effect in quantum spin liquids with spinon Fermi surfaces
• A Kondo route to spin inhomogeneities in the honeycomb Kitaev model
• Quantum correlations and entanglement in a Kitaev-type spin chain
• Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state
• Anyon dynamics in field-driven phases of the anisotropic Kitaev model
• Zero energy and chiral edge modes in a p-wave magnetic spin model
• Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Majorana correlations in the Kitaev model with ordered-flux structures
• A Possible Fermi liquid in the lightly doped Kitaev spin liquid
• Analytic calculation of the vison gap in the Kitaev spin liquid
• Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Stable Parton Fermi Surface
• Low temperature properties in the Bilayer Kitaev model
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Emergent orbital magnetization in Kitaev quantum magnets
• Phononic-magnetic dichotomy of the thermal Hall effect in the Kitaev-Heisenberg candidate material Na${}_2$Co${}_2$TeO${}_6$
• Fractionalized Prethermalization in a Driven Quantum Spin Liquid
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• Insights into the Anisotropic Spin-$S$ Kitaev Chain
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• Antiferromagnetic resonance in the cubic iridium hexahalides (NH${}_4$)${}_2$IrCl${}_6$ and K${}_2$IrCl${}_6$
• Fermionic approach to variational quantum simulation of Kitaev spin models
• Probing quantum spin liquids in equilibrium using the inverse spin Hall effect
• Tuning into the Kitaev spin liquid phase:A spin model on the honeycomb lattice with two types of Heisenberg exchange couplings
• Ground-state properties of the $K-\Gamma$ model on a honeycomb lattice
• Variational Monte Carlo Method in the Presence of Spin-Orbit Interaction and Its Application to the Kitaev and Kitaev-Heisenberg Model
• Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting
• Majorana edge magnetization in the Kitaev honeycomb model
• Photoinduced Floquet topological magnons in Kitaev magnets
• Sub-gap optical response across the structural phase transition in van der Waals layered α-RuCl${}_3$
• Entanglement and Majorana edge states in the Kitaev model
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Probing Majorana wavefunctions in Kitaev honeycomb spin liquids with second-order two-dimensional spectroscopy
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• Electric-field control of magnetic anisotropies: applications to Kitaev spin liquids and topological spin textures
• Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field
• Exact chiral spin liquid state in a Kitaev type spin model
• Compass and Kitaev models -- Theory and Physical Motivations
• Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields
• Phases and Quantum Phase Transitions in an Anisotropic Ferromagnetic Kitaev-Heisenberg-$\Gamma$ Magnet
• Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid
• Gauge field entanglement of Kitaev's honeycomb model
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model
• Evidences for the random singlet phase in a new honeycomb iridate SrIr${}_2$O${}_{6-\delta }$
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements
• Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
• Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models
• Quantum paramagnetism in the hyperhoneycomb Kitaev magnet $\beta$-ZnIrO${}_3$
• Incarnation of Majorana Fermions in Kitaev Quantum Spin Lattice
• Role of Majorana fermions in spin transport of anisotropic Kitaev model
• Block entropy for Kitaev-type spin chains in a transverse field
• Dynamics of fractionalized mean-field theories: consequences for Kitaev materials
• Driven one-dimensional noisy Kitaev chain
• Asymmetric modulation of Majorana excitation spectra and nonreciprocal thermal transport in the Kitaev spin liquid under a staggered magnetic field
• Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Quantum dimer model containing Rokhsar-Kivelson point expressed by spin-1/2 Heisenberg antiferromagnets
• Low-energy Majorana states in spin-liquid transitions in a three-dimensional Kitaev model
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model
• Defect production and quench dynamics in the three-dimensional Kitaev model
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Bound states of fractionalized excitations in a modulated Kitaev spin liquid
• Perturbed Kitaev model: excitation spectrum and long-ranged spin correlations
• Engineering the Kitaev spin liquid in a quantum dot system
• Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity
• Probing Kitaev Models on Small Lattices
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Quantum phase transitions in spin-1 compass chains
• Valence bond fluctuations in the Kitaev spin model
• Exploration of trivial and non-trivial electronic phases and of collinear and non-collinear magnetic phases in low-spin d${}^5$ perovskites
• Interedge spin resonance in the Kitaev quantum spin liquid
• Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation
• Machine learning reveals features of spinon Fermi surface
• Dimensional reduction of Kitaev spin liquid at quantum criticality
• Gauge symmetry of excited states in projected entangled-pair state simulations
• Induction of Large Magnetic Anisotropy Energy and Formation of Multiple Dirac States in SrIrO${}_3$ Films: Role of correlation and spin-orbit coupling
• Magnetic order through Kondo coupling to quantum spin liquids
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• High temperature dynamics in quantum compass models
• Maximal distant entanglement in Kitaev tube
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• Gapless state of interacting Majorana fermions in a strain-induced Landau level
• Response and phase transition of a Kitaev spin liquid in a local magnetic field
• Dominant Kitaev interaction and field-induced quantum phase transitions in triangular-lattice KCeSe2
• Emergence of a Dimer-Dimer Interaction in the Low-Energy Effective Quantum-Dimer Model of a Diamond-Like-Decorated Square-Lattice Heisenberg Antiferromagnets with Further Neighbor Couplings
• Digital Quantum Simulation of the Kitaev Quantum Spin Liquid
• Two-stage evolution of magnetic correlations in spiral spin liquid material, Ca${}_{10}$Cr${}_7$O${}_{28}$
• Finite-momentum energy dynamics in a Kitaev magnet
• Emergent Quadrupolar Order in the Spin-$1/2$ Kitaev-Heisenberg Model
• Controlling the RKKY interaction and heat transport in a Kitaev spin liquid via $Z_2$ flux walls
• Spin-orbital liquid in Ba${}_3$CuSb${}_2$O${}_9$ stabilized by oxygen holes
• Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Fractionalized Superconductivity Mediated by Majorana Fermions in the Kitaev-Kondo Lattice
• One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part II -- dynamics of Majorana fermions
• Spin correlation and Majorana spectrum in chiral spin liquids in a decorated-honeycomb Kitaev model
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Topological Aspects of Antiferromagnets
• Topological Characterization of Kitaev Spin Nanoribbons with Ordered Flux Configurations
• Quantum phase transitions in the Kitaev--Heisenberg model on a single hexagon
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects
• Spin-Spin Correlations in the Kitaev Model at Finite Temperatures: Approximate and Exact Results via Green's Function Equation of Motion
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• A chain of strongly correlated SU(2)_4 anyons: Hamiltonian and Hilbert space of states
• Strain-induced Landau levels of Majorana fermions in an anisotropically interacting Kitaev model on a honeycomb lattice
• Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Coexistence of static and dynamic local magnetic fields in an S = 3/2 honeycomb lattice antiferromagnet Co2Te3O8
• Static and Dynamical Spin Correlations in the Kitaev Model at Finite Temperatures via Green's Function Equation of Motion
• Long-range spin correlations in a honeycomb spin model with magnetic field
• Quantum theory of spin waves for Helical ground states in Hollandite lattice
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Analysis of the behavior of singlet pairs in inorganic crystal XOCl(X=Ti,Bi)
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet
• Majorana Signatures in Planar Tunneling through a Kitaev Spin Liquid
• Three-dimensional spin-orbital liquids
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Magnetic field effects on the Kitaev model coupled to environment