Entanglement entropy in the Lipkin-Meshkov-Glick model

Abstract

We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spins half embedded in a magnetic field. This entropy displays a singularity at the critical point that we study as a function of the interaction anisotropy, the magnetic field, and the system size. Results emerging from our analysis are surprisingly similar to those found for the one-dimensional XY chain.

5 pages, 5 figures, published version

References in corpus (25)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement in a simple quantum phase transition
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Entanglement and the Phase Transition in Single Mode Superradiance
• Applied Conformal Field Theory
• Quantum Superposition States of Bose-Einstein Condensates
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Entanglement entropy of random quantum critical points in one dimension
• Entanglement in a second order quantum phase transition
• Entanglement in XY Spin Chain
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement in a first order quantum phase transition
• Entanglement dynamics in the Lipkin-Meshkov-Glick model
• Fine-grained entanglement loss along renormalization group flows
• Generation of many-particle entanglement in an ion trap by adiabatic ground-state transitions
• Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model
• Universality of Entanglement and Quantum Computation Complexity
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• Adiabatic quantum computation and quantum phase transitions
• Concurrence in the two dimensional XXZ- and transverse field Ising-models

Cited by in corpus (149)

• Area laws for the entanglement entropy - a review
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Entanglement entropy and conformal field theory
• Fidelity approach to quantum phase transitions
• Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system
• Chopped random-basis quantum optimization
• Entanglement Entropy dynamics in Heisenberg chains
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Entanglement growth in quench dynamics with variable range interactions
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• A short review on entanglement in quantum spin systems
• Bridging entanglement dynamics and chaos in semiclassical systems
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Entanglement Entropy beyond the Free Case
• Entanglement entropy in collective models
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Universality of the negativity in the Lipkin-Meshkov-Glick model
• Entanglement dynamics in short and long-range harmonic oscillators
• Concurrence in collective models
• Finite-temperature mutual information in a simple phase transition
• Entanglement and fluctuations in the XXZ model with power-law interactions
• Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement
• Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity
• Quantum Fidelity and Thermal Phase Transitions
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Entanglement and Many-Body effects in Collective Neutrino Oscillations
• Proposal for quantum many-body simulation and torsional matter-wave interferometry with a levitated nanodiamond
• Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling
• Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model
• Information scrambling vs. decoherence -- two competing sinks for entropy
• Increasing of entanglement entropy from pure to random quantum critical chains
• Mutual information in classical spin models
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Area law and vacuum reordering in harmonic networks
• Separability of diagonal symmetric states: a quadratic conic optimization problem
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Thermalization in a periodically driven fully-connected quantum Ising ferromagnet
• Dynamical Phase Transitions in models of Collective Neutrino Oscillations
• Continuous unitary transformations in two-level boson systems
• Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model
• Many-body Dynamics in Monitored Atomic Gases Without Post-Selection Barrier
• Classification of Entanglement in Symmetric States
• Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
• Phase space geometry and optimal state preparation in quantum metrology with collective spins
• Particle partitioning entanglement in itinerant many-particle systems
• Effects of excited state quantum phase transitions on system dynamics
• Quantum Critical Dynamics of A Qubit Coupled to An Isotropic Lipkin-Meshkov-Glick Bath
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Simulating the Lipkin-Meshkov-Glick model in a hybrid quantum system
• Multi-Body Entanglement and Information Rearrangement in Nuclear Many-Body Systems
• Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model
• Bell correlations at Ising quantum critical points
• The Lipkin-Meshkov-Glick model with Markovian dissipation -- A description of a collective spin on a metallic surface
• Entanglement and Density Matrix of a Block of Spins in AKLT Model
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Quantum entanglement entropy and classical mutual information in long-range harmonic oscillators
• Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
• Nonstabilizerness of Permutationally Invariant Systems
• The Hong-Ou-Mandel effect with atoms
• Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
• Entanglement Storage Units
• Fermionic entanglement in the Lipkin model
• Entanglement in Valence-Bond-Solid States
• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
• Spin squeezing and entanglement via finite-dimensional discrete phase-space description
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Quantum Simulations of SO(5) Many-Fermion Systems using Qudits
• On the Entanglement Between Interacting Scalar Field Theories
• Complexity in the Lipkin-Meshkov-Glick Model
• Theory of robust quantum many-body scars in long-range interacting systems
• Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model
• Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
• Magnetic field dependence of the entanglement entropy of one dimensional spin systems in quantum phase transition induced by a quench
• Bose-Hubbard dimers, Viviani's windows and pendulum dynamics
• Monogamy and ground-state entanglement in highly connected systems
• Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Genuine Multipartite Correlations Distribution in the Criticality of Lipkin-Meshkov-Glick Model
• Measurement-induced phase transitions in monitored infinite-range interacting systems
• Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state
• Entanglement in permutation symmetric states, fractal dimensions, and geometric quantum mechanics
• Block Entanglement Entropy of Ground States with Long-Range Magnetic Order
• Quantifying quantumness of correlations using Gaussian Rényi-2 entropy in optomechanical interfaces
• Thermal entanglement of spins in mean-field clusters
• $q$-analog qudit Dicke states
• Two-Point Entanglement Near a Quantum Phase Transition
• Evaluation of ground state entanglement in spin systems with the random phase approximation
• Wehrl entropy production rate across a dynamical quantum phase transition
• Frustration, Area Law, and Interference in Quantum Spin Models
• Entanglement entropy in long-range harmonic oscillators
• Entanglement entropy of the long-range Dyson hierarchical model
• Dynamics of genuine multipartite correlations in open quantum systems
• Rotor/spin-wave theory for quantum spin models with U(1) symmetry
• Eigenstate entanglement in integrable collective spin models
• Molecular spectra in collective Dicke states
• Quantum statistics of the collective excitations of an atomic ensemble inside a cavity
• Qudit Dicke state preparation
• Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench
• Quantum Physics in Connected Worlds
• Unraveling Dicke Superradiant Decay with Separable Coherent Spin States
• Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
• A family of many-body models which are exactly solvable analytically
• Spin-s Dicke states and their preparation
• Matrix product state approach to a frustrated spin chain with long-range interactions
• Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition
• Semiclassical bifurcations and quantum trajectories: a case study of the open Bose-Hubbard dimer
• Dicke states as matrix product states
• Entanglement and entropy production in coupled single-mode Bose-Einstein condensates
• Supersymmetric spin chains with non-monotonic dispersion relation: criticality and entanglement entropy
• Origin of Topological Order in a Cooper Pair Insulator
• The Thermodynamic Limit of Spin Systems on Random Graphs
• Symmetric quantum states: a review of recent progress
• Statistical and dynamical aspects of quantum chaos in a kicked Bose-Hubbard dimer
• Scaling of the von Neumann entropy across a finite temperature phase transition
• Entanglement witness via symmetric two-body correlations
• Phase diagram of 1+1D Abelian-Higgs model and its critical point
• Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
• Wiseman-Milburn Control for the Lipkin-Meshkov-Glick Model
• An operational definition of quantum information scrambling
• Inherent quantum resources in stationary spin chains
• Experimental demonstration of spontaneous symmetry breaking with emergent multi-qubit entanglement
• A Floquet analysis perspective of driven light-matter interaction models
• Entanglement of Valence-Bond-Solid on an Arbitrary Graph
• Block Spin Density Matrix of the Inhomogeneous AKLT Model
• Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model
• Entanglement and area laws in weakly correlated gaussian states
• Entanglement of condensed magnons via momentum-space fragmentation
• The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain
• Short-time expansion of Heisenberg operators in open collective quantum spin systems
• Genuine $k$-partite correlations and entanglement in the ground state of the Dicke model for interacting qubits
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• Noise Effects on Diabatic Quantum Annealing Protocols
• Scale invariant distribution functions in quantum systems with few degrees of freedom
• Investigating Lipkin-Meshkov-Glick Model and Criticality-Enhanced Metrology in a Coherent Ising Machine
• Decoherence of a quantum memory coupled to a collective spin bath
• On Emergent Geometry from Entanglement Entropy in Matrix theory
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type
• Entanglement Entropy in Many-Fermion System
• Mutual information in interacting spin systems