Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

Abstract

We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped A phase with Abelian anyon excitations to a gapless B phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be $1/\xi =2{\sinh }^{-1}[\sqrt{2J_z-1}/(1-J_z)]$, which diverges around the critical point $J_z=(1/2{)}^{+}$.

arXiv comment7 pages, 6 figures

References in corpus (28)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• String-net condensation: A physical mechanism for topological phases
• Ground state overlap and quantum phase transitions
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Quantum orders in an exact soluble model
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Mixed-state fidelity and quantum criticality at finite temperature
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Ground state fidelity from tensor network representations
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Quantum fidelity and quantum phase transitions in matrix product states
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Ground-state fidelity in one-dimensional gapless model
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Emergent Fermions and Anyons in the Kitaev Model
• Mosaic spin models with topological order
• Fidelity Between Partial States as Signature of Quantum Phase Transitions
• Creation and Manipulation of Anyons in the Kitaev Model
• The Wavefunction of an Anyon

Cited by in corpus (105)

• Fidelity approach to quantum phase transitions
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Quantum enhanced measurements without entanglement
• Geometry of quantum phase transitions
• Classifying and measuring the geometry of the quantum ground state manifold
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Abelian and Non-Abelian Quantum Geometric Tensor
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Coherent and dissipative dynamics at quantum phase transitions
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
• Characterization of topological states via dual multipartite entanglement
• Quantum Fidelity and Thermal Phase Transitions
• Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Scaling dimension of fidelity susceptibility in quantum phase transitions
• Measurement of Topological Order based on Metric-Curvature Correspondence
• Fidelity in topological quantum phases of matter
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models
• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Oscillating fidelity susceptibility near a quantum multicritical point
• Scaling of ground state fidelity in the thermodynamic limit: XY model and beyond
• Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model
• Information Geometry and Quantum Phase Transitions in the Dicke Model
• Reduced fidelity in topological quantum phase transitions
• Ground-state fidelity at first-order quantum transitions
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Generalized fidelity susceptibility at phase transitions
• Fidelity Susceptibility in the Quantum Rabi Model
• Non-local correlations in the Haldane phase for an XXZ spin-1 chain: A perspective from infinite matrix product state representation
• Scaling of the fidelity susceptibility in a disordered quantum spin chain
• Spectral function and fidelity susceptibility in quantum critical phenomena
• Fidelity susceptibility near topological phase transitions in quantum walks
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Fidelity as a probe for a deconfined quantum critical point
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Fidelity susceptibility of the anisotropic $XY$ model: The exact solution
• Quantum information approach to the quantum phase transition in the Kitaev honeycomb model
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Topological quantum phase transition in an extended Kitaev spin model
• Quantum phases of disordered flatband lattice fractional quantum Hall systems
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Revealing Chern number from quantum metric
• Universal sub-leading terms in ground state fidelity
• One and two-dimensional quantum models: quenches and the scaling of irreversible entropy
• From Classical to Quantum Information Geometry: A Guide for Physicists
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Entanglement modes and topological phase transitions in superconductors
• Universal fidelity near quantum and topological phase transitions in finite 1D systems
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Reduced fidelity in Kitaev honeycomb model
• Novel Approach to Unveil Quantum Phase Transitions Using Fidelity Map
• Thermal states of the Kitaev honeycomb model: a Bures metric analysis
• Detecting Topological Order with Ribbon Operators
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Density-functional fidelity approach to quantum phase transitions
• The three site interacting spin chain in staggered field: Fidelity vs Loschmidt echo
• Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Quantum distance and the Euler number index of the Bloch band in a 1D spin model
• Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules
• Fidelity susceptibility of one-dimensional models with twisted boundary conditions
• Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Finite temperature geometric properties of the Kitaev honeycomb model
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition
• Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study
• Entanglement and Majorana edge states in the Kitaev model
• Operator Quantum Geometric Tensor and Quantum Phase Transitions
• Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model
• Fidelity susceptibility and Loschmidt echo for generic paths in a three spin interacting transverse Ising model
• Quantum geometrical properties of topological materials
• Exotic phase diagram of a topological quantum system
• Classical criticality establishes quantum topological order
• Diagnosing Topological Phase Transitions in 1D Superconductors using Berry Singularity Markers
• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature
• Reduced fidelity approach for quantum phase transitions in spin-1/2 dimerized Heisenberg chains
• The Loschmidt Index
• On critical properties of Berry curvature in Kitaev honeycomb model
• Vanishing k-space fidelity and phase diagram's bulk-edge-bulk correspondence
• Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals
• Valence bond fluctuations in the Kitaev spin model
• Foliated order parameter in a fracton phase transition
• State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain
• Dynamical scaling laws in the quantum $q$-state clock chain
• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Fidelity, Rosen-Zener Dynamics, Entropy and Decoherence in one dimensional hard-core bosonic systems
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Geometric phase in the Kitaev honeycomb model and scaling behavior at critical points
• Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice
• Quantum simulation and ground state preparation for the honeycomb Kitaev model
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Theory of Berry Singularity Markers: Diagnosing Topological Phase Transitions via Lock-In Tomography