Entanglement entropy and entanglement spectrum of the Kitaev model

Abstract

In this paper, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S=S_G+S_F, with S_F the entanglement entropy of a free Majorana fermion system and S_G that of a Z_2 gauge field. The Z_2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the non-local entanglement carried by the Z_2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the states with and without topologically protected gapless entanglement spectrum.

4.0 pages + supplementary material, published version in Phys. Rev. Lett

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of topological insulators and superconductors
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Entanglement entropy in fermionic Laughlin states
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• The entanglement gap and a new principle of adiabatic continuity
• Entanglement and topological entropy of the toric code at finite temperature
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Bipartite entanglement entropy in fractional quantum Hall states
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• A $\Gamma$-matrix generalization of the Kitaev model
• Three-dimensional topological phase on the diamond lattice
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking

Cited by in corpus (187)

• Towards a derivation of holographic entanglement entropy
• Quantum entanglement in condensed matter systems
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Relative Entropy and Holography
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Entanglement entropy: holography and renormalization group
• Bulk-Edge Correspondence in the Entanglement Spectra
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Entanglement entropy of critical spin liquids
• Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field
• How universal is the entanglement spectrum?
• Power-Law Entanglement Spectrum in Many-Body Localized Phases
• Renyi Entropies for Free Field Theories
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Topological Order and Semions in a Strongly Correlated Quantum Spin Hall Insulator
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Physical solutions of the Kitaev honeycomb model
• Twisted and untwisted negativity spectrum of free fermions
• Negativity spectrum of one-dimensional conformal field theories
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• A simple fermionic model of deconfined phases and phase transitions
• Entanglement spectroscopy on a quantum computer
• Probing Hawking radiation through capacity of entanglement
• Aspects of capacity of entanglement
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Twist operators in higher dimensions
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry
• Replica wormholes and capacity of entanglement
• Intrinsic Mixed-state Topological Order
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Bound states and entanglement in the excited states of quantum spin chains
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair States: spinon and vison coherence lengths, topological entropy and gapless edge modes
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• A Holographic Proof of Rényi Entropic Inequalities
• Theory of the Kitaev model in a [111] magnetic field
• Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Critical behaviors of non-stabilizerness in quantum spin chains
• Von Neumann Entropy Spectra and Entangled Excitations in Spin-Orbital Models
• Entanglement Entropy of U(1) Quantum Spin Liquids
• Density-Matrix Renormalization Group Study of Extended Kitaev-Heisenberg Model
• Universal entanglement spectrum in gapless symmetry protected topological states
• Notes on Entanglement in Abelian Gauge Theories
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• Negativity Spectrum in the Random Singlet Phase
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Multipartitioning topological phases by vertex states and quantum entanglement
• Measuring entanglement entropy and its topological signature for phononic systems
• Multivariate trace estimation in constant quantum depth
• Eigenstate capacity and Page curve in fermionic Gaussian states
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Anyonic Entanglement and Topological Entanglement Entropy
• Position momentum Duality in the Entanglement Spectrum of Free Fermions
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Polarization and entanglement spectrum in non-hermitian systems
• Localised zero-energy modes in the Kitaev model with vacancy-disorder
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Capacity of Entanglement for Non-local Hamiltonian
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Capacity of Entanglement in Local Operators
• Capacity of entanglement in random pure state
• Critical light-matter entanglement at cavity mediated phase transition
• Exactly Solvable Topological Chiral Spin Liquid with Random Exchange
• Free-fermion descriptions of parafermion chains and string-net models
• Majorana Landau Level Raman Spectroscopy
• Kondo Breakdown via Fractionalization in a Frustrated Kondo Lattice Model
• Density-Matrix Renormalization Group Study of Kitaev--Heisenberg Model on a Triangular Lattice
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Entanglement Entropy & Anomaly Inflow
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Cornering gapless quantum states via their torus entanglement
• Gravitational back-reaction is magical
• Topological order, entanglement, and quantum memory at finite temperature
• Tensor Network Implementation of Bulk Entanglement Spectrum
• The variance of relative surprisal as single-shot quantifier
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• Entanglement in a second order topological insulator on a square lattice
• Global entanglement in a topological quantum phase transition
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• Fractionalized Prethermalization in a Driven Quantum Spin Liquid
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Diagnosing Topological Edge States via Entanglement Monogamy
• Entanglement in Weakly Coupled Lattice Gauge Theories
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Entanglement spectrum and entropy in Floquet topological matter
• Average capacity of quantum entanglement
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Stronger speed limit for observables: Tight bound for the capacity of entanglement, the modular Hamiltonian and the charging of a quantum battery
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Entanglement and Majorana edge states in the Kitaev model
• Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Gauge field entanglement of Kitaev's honeycomb model
• Entanglement dualities in supersymmetry
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Entanglement sum rules in exactly solvable models
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements
• Entanglement-assisted local operations and classical communications conversion in the quantum critical systems
• Wilsonian Effective Action and Entanglement Entropy
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• On the relation of the entanglement spectrum to the bulk polarization
• Unified multivariate trace estimation and quantum error mitigation
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• Topological entanglement entropy of three-dimensional Kitaev model
• Predicting topological quantum phase transition from dynamics via multisite entanglement
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation
• Confinement transition in a Kitaev-like honeycomb model with bond anisotropy
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Edge--Entanglement correspondence for gapped topological phases with symmetry
• On Quantum Entanglement in Topological Phases on a Torus
• Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states
• Squashed entanglement in one-dimensional quantum matter
• Vanishing k-space fidelity and phase diagram's bulk-edge-bulk correspondence
• Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems
• Reentrance of Topological Phase in Spin-1 Frustrated Heisenberg Chain
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Computing quantum magic of state vectors
• Quenching the Kitaev honeycomb model
• Valence bond fluctuations in the Kitaev spin model
• Entanglement in 3D Kitaev Spin Liquids
• Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases
• Entanglement transition through Hilbert-space localization
• Majorization relation in quantum critical systems
• Chiral spin liquid in a ${\mathbb{Z}}_3$ Kitaev model
• Characterization of photoexcited states in the half-filled one-dimensional extended Hubbard model assisted by machine learning
• Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields
• Entanglement in topological systems
• Hagedorn transition and topological entanglement entropy
• Edge Theories for Anyon Condensation Phase Transitions
• On integrable matrix product operators with bond dimension $D=4$
• Phase diagram of quantum critical system via local convertibility of ground state
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair
• Entanglement, subsystem particle numbers and topology in free fermion systems
• Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry
• Diagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Gravity dualities of quantum distances
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• From Hermitian critical to non-Hermitian point-gapped phases
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Inverse Hamiltonian design of highly-entangled quantum systems
• 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 II -- dynamics of Majorana fermions
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• A useful way to obtain the central charge of entanglement Hamiltonian -- Nested entanglement entropy
• Towards Entanglement Entropy of Random Large-N Theories
• Entanglement capacity of fermionic Gaussian states
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• Dynamical Geometry of the Haldane Model under a Quantum Quench
• Topological Properties and Characterizations
• Entanglement spectrum of gapless topological phases: a case study with topological superconductors
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair
• Unveiling topological order through multipartite entanglement
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes
• Exact Mappings in Condensed Matter Physics