Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model

Abstract

We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents for the energy gap, the ground state energy, the magnetization, and the spin-spin correlation functions. Finally, we discuss the behavior of the two-spin entanglement in the vicinity of the phase transition.

4 pages, published version

References in corpus (12)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Quantum Superposition States of Bose-Einstein Condensates
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Entanglement in a second order quantum phase transition
• Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
• Entanglement in a first order quantum phase transition
• Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
• Flow equations for band--matrices
• The Quartic Oscillator: a Non-Perturbative Study by Continuous Unitary Transformations
• Hamiltonian Flow Equations for the Lipkin Model

Cited by in corpus (193)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Fidelity approach to quantum phase transitions
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Coherent and Collective Quantum Optical Effects in Mesoscopic Systems
• Measuring multipartite entanglement via dynamic susceptibilities
• Long-range interacting quantum systems
• 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
• Quantum phase transitions in the interacting boson model
• Entanglement entropy in the Lipkin-Meshkov-Glick model
• Thermometry in the quantum regime: Recent theoretical progress
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Finite-Size Scaling Exponents in the Dicke Model
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
• Entanglement dynamics in the Lipkin-Meshkov-Glick model
• Quantum critical metrology
• Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
• Quantum metrology in Lipkin-Meshkov-Glick critical systems
• Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Probing the Dynamics of Superradiant Quantum Phase Transition in a Single Trapped-Ion
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Bridging entanglement dynamics and chaos in semiclassical systems
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Entanglement Entropy beyond the Free Case
• Cost of counterdiabatic driving and work output
• Entanglement entropy in collective models
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Universality of the negativity in the Lipkin-Meshkov-Glick model
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Concurrence in collective models
• Dynamical critical scaling of long-range interacting quantum magnets
• Finite-temperature mutual information in a simple phase transition
• Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model
• Origin of the slow growth of entanglement entropy in long-range interacting spin systems
• Quantum Fidelity and Thermal Phase Transitions
• Multipartite Entanglement at Finite Temperature
• Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator
• Counterdiabatic driving in the quantum annealing of the $p$-spin model: a variational approach
• Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling
• Collective performance of a finite-time quantum Otto cycle
• Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model
• Scaling dimension of fidelity susceptibility in quantum phase transitions
• Information scrambling vs. decoherence -- two competing sinks for entropy
• New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Kuramoto dynamics in Hamiltonian systems
• Fully-connected network of superconducting qubits in a cavity
• Generating stable spin squeezing by squeezed-reservoir engineering
• Universal anti-Kibble-Zurek scaling in fully-connected systems
• Flow Equations and Normal Ordering. A Survey
• Probing quantum correlations in many-body systems: a review of scalable methods
• Quantum correlations in the collective spin systems
• Global and local thermometry schemes in coupled quantum systems
• Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Time evolution and decoherence of a spin-1/2 particle coupled to a spin bath in thermal equilibrium
• Dynamical and excited-state quantum phase transitions in collective systems
• Dual algebraic structures for the two-level pairing model
• A scalar two-level boson model to study the IBM phase diagram in the Casten triangle
• Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity
• Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state
• Geometric phases and quantum phase transitions
• Microwave photon detection at parametric criticality
• Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model
• Quantum Criticality in a Bosonic Josephson Junction
• Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer
• Finite-size scaling exponents and entanglement in the two-level BCS model
• Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates
• Continuous unitary transformations in two-level boson systems
• Squeezing by Critical Speeding-up: Applications in Quantum Metrology
• Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate
• Finite-size scaling exponents in the interacting boson model
• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions
• Probing quantum criticality and symmetry breaking at the microscopic level
• Phase space geometry and optimal state preparation in quantum metrology with collective spins
• Exponential precision by reaching a quantum critical point
• Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
• Quantum Critical Dynamics of A Qubit Coupled to An Isotropic Lipkin-Meshkov-Glick Bath
• Quantum Critical Behavior of Two Coupled Bose-Einstein Condensates
• Untangling entanglement and chaos
• Universal driven critical dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates
• The extended Heine-Stieltjes polynomials associated with a special LMG model
• Bell correlations at Ising quantum critical points
• Finite-size scaling analysis in the two-photon Dicke model
• The Lipkin-Meshkov-Glick model with Markovian dissipation -- A description of a collective spin on a metallic surface
• Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model
• Non-equilibrium criticality in quench dynamics of infinite-range spin models
• Machine learning time-local generators of open quantum dynamics
• Harnessing non-adiabatic excitations promoted by a quantum critical point
• Geometric Phase and Quantum Phase Transition in the Lipkin-Meshkov-Glick model
• Fermionic entanglement in the Lipkin model
• Heisenberg Uncertainty Principle as Probe of Entanglement Entropy: Application to Superradiant Quantum Phase Transitions
• Protecting and Enhancing Spin Squeezing via Continuous Dynamical Decoupling
• Shortcuts to adiabaticity in the infinite-range Ising model by mean-field counter-diabatic driving
• Virtues and limitations of the truncated Holstein-Primakoff description of quantum rotors
• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• Dynamical Scaling Laws of Out-of-Time-Ordered Correlators
• Finite-size criticality in fully connected spin models on superconducting quantum hardware
• Spin squeezing in dipolar spinor condensates
• Spin squeezing and entanglement via finite-dimensional discrete phase-space description
• Critical quantum thermometry and its feasibility in spin systems
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Complexity in the Lipkin-Meshkov-Glick Model
• Identifying the order of a quantum phase transition by means of Wehrl entropy in phase-space
• Entanglement in quantum catastrophes
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects
• Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model
• Density-functional fidelity approach to quantum phase transitions
• Description of thermal entanglement with the static path plus random-phase approximation
• Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
• On the Thermodynamic Limit of the Lipkin Model
• Thermal entanglement in fully connected spin systems and its RPA description
• On the finite size behavior of quantum collective spin systems
• Uncertain Quantum Critical Metrology: From Single to Multi Parameter Sensing
• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Genuine Multipartite Correlations Distribution in the Criticality of Lipkin-Meshkov-Glick Model
• Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions
• Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state
• Optically controlled spin-glasses in multi-qubit cavity systems
• Wehrl entropy production rate across a dynamical quantum phase transition
• Two-Point Entanglement Near a Quantum Phase Transition
• Thermal entanglement of spins in mean-field clusters
• Quantum delocalization on correlation landscape: The key to exponentially fast multipartite entanglement generation
• Quantum Magnetism with Mesoscopic Bose-Einstein Condensates
• Ultrafast critical ground state preparation via bang-bang protocols
• Double symmetry breaking and 2D quantum phase diagram in spin-boson systems
• Mesoscopic Bose-Einstein condensates as quantum simulators
• Optical signatures of quantum phase transitions in a light-matter system
• Two-spin subsystem entanglement in spin 1/2 rings with long range interactions
• Symmetry-Protected Quantum Adiabatic Evolution in Spontaneous Symmetry-Breaking Transitions
• Critical exponents for an impurity in a bosonic Josephson junction: Position measurement as a phase transition
• Measuring out-of-time-ordered correlation functions with a single impurity qubit in a bosonic Josephson junction
• Quantum adiabatic cycles and their breakdown
• Anomalous criticality with bounded fluctuations and long-range frustration induced by broken time-reversal symmetry
• Fidelity, susceptibility and critical exponents in the Dicke model
• Exact scaling of geometric phase and fidelity susceptibility and their breakdown across the critical points
• Critical steady states of all-to-all squeezed and driven superradiance: An analytic approach
• Polaron-transformed dissipative Lipkin-Meshkov-Glick Model
• Searching for pairing energies in phase space
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• The classical limit of mean-field quantum spin systems
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Quantum phase transitions in the triangular coupled-top model
• Optimal Spin Squeezed Steady State induced by the dynamics of non-hermtian hamiltonians
• Critical phenomena in light-matter systems with collective matter interactions
• Quantum discord and related measures of quantum correlations in XY chains
• Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures
• Density Matrix Functional Theory for the Lipkin model
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Spin-glasses in optical cavity
• Wiseman-Milburn Control for the Lipkin-Meshkov-Glick Model
• Quantum criticality driven by the cavity coupling in Rabi-dimer model
• Transport through a quantum critical system: A thermodynamically consistent approach
• Quantum Phase Transitions in a Generalized Dicke Model
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Strong-coupling expansion and effective hamiltonians
• Entanglement and its facets in condensed matter systems
• A Floquet analysis perspective of driven light-matter interaction models
• Quantum Simulation of Quantum Phase Transitions Using the Convex Geometry of Reduced Density Matrices
• Two-photon statistics of nonclassical radiation in the dissipative finite-size Dicke model
• The SU(N) Fermi-Hubbard Model on two sites: Bethe Ansatz solution and Quantum Phase Transition of the Lipkin-Meshkov-Glick Model in the large-N limit
• On the Geodesic Nature of Wegner's Flow
• Extended Lipkin-Meshkov-Glick Hamiltonian
• Quantum Hopfield Model with Dilute Memories
• Quantum Phase Transitions in periodically quenched systems
• Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to $N$-atom Dicke model
• Precision magnetometry exploiting excited state quantum phase transitions
• Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model
• Scale invariant distribution functions in quantum systems with few degrees of freedom
• Scaling Properties of the Lipkin Model at the Critical Point
• Non-equilibrium entanglement in a driven Dicke model
• Stability of emergent time periodicity in a few-body interacting system
• Symmetry conserving Coupled Cluster Doubles wave function and the Self-Consistent odd particle number RPA
• Quantum information scrambling in adiabatically-driven critical systems
• Effects of dynamical paths on the energy gap and the corrections to free energy in path integrals of mean-field quantum spin systems
• Entanglement distribution in fermion model with long-range interaction
• Quantum Criticality in the infinite-range Transverse Field Ising Model
• Investigating Lipkin-Meshkov-Glick Model and Criticality-Enhanced Metrology in a Coherent Ising Machine
• Efficient approximation for global functions of matrix product operators
• Generating Generalised Ground-State Ansatzes from Few-Body Examples
• Quantum transitions, ergodicity, and quantum scars in the coupled top model
• Multipartite entanglement in quantum phase transitions
• Bootstrapping entanglement in quantum spin systems
• Quantum sensing with discrete time crystals in the Lipkin-Meshkov-Glick Model
• Mutual information in interacting spin systems
• Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions