Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states
arXiv:2207.04842 · doi:10.1103/PhysRevResearch.5.013158
Abstract
We use entanglement witnesses to detect entanglement in the XY chain in thermal equilibrium and determine the temperature bound below which the state is detected as entangled. We consider the entanglement witness based on the Hamiltonian. Such a witness detects a state as entangled if its energy is smaller than the energy of separable states. We also consider a family of entanglement witnesses related to the entanglement negativity of the state. We test the witnesses in infinite and finite systems. We study how the temperature bounds obtained are influenced by a quantum phase-transition or a disorder line in the ground state. Very strong finite-size corrections are observed in the ordered phase due to the presence of a quasi-degenerate excitation. We also study the postquench states in the thermodynamic limit after a quench when the parameters of the Hamiltonian are changed suddenly. In the case of the Ising model, we find that the mixed postquench state is detected as entangled by the two methods if the parameters of the Hamiltonian before and after the quench are close to each other. We find that the two witnesses give qualitatively similar results, showing that energy-based entanglement witnesses are efficient in detecting the nearest-neighbor entanglement in spin chains in various circumstances. For other XY models, we find that the negativity based witnesses also detect states in some parameter regions where the energy-based witness does not, in particular, if the quench is performed from the paramagnetic phase to the ferromagnetic phase and vice versa. The domains in parameter space corresponding to postquench states detected as entangled by the energy-based witness have been determined analytically, which stresses further the utility of our method.
arXiv commentSomewhat extended version, references added
References in corpus (81)
- Quantum entanglement
- Many-Body Physics with Ultracold Gases
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Nonequilibrium dynamics of closed interacting quantum systems
- Entanglement detection
- Scaling of Entanglement close to a Quantum Phase Transitions
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Entanglement in a simple quantum phase transition
- Separability criterion and inseparable mixed states with positive partial transposition
- Experimental One-Way Quantum Computing
- Scalable multi-particle entanglement of trapped ions
- Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Time-dependence of correlation functions following a quantum quench
- 14-qubit entanglement: creation and coherence
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
- Light-cone-like spreading of correlations in a quantum many-body system
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Bell Inequalities and the Separability Criterion
- Optimization of entanglement witnesses
- Generalized Gibbs ensemble in integrable lattice models
- Classification of mixed three-qubit states
- The Luttinger model following a sudden interaction switch-on
- Witnessing multipartite entanglement
- Complete Generalized Gibbs Ensemble in an interacting Theory
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- Dephasing and the steady state in quantum many-particle systems
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
- Entanglement Certification From Theory to Experiment
- Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
- Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state
- Quasilocal charges in integrable lattice systems
- Quench dynamics across quantum critical points
- Strongly correlated fermions after a quantum quench
- Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
- Experimental entanglement of a six-photon symmetric Dicke state
- Experimental Analysis of a 4-Qubit Cluster State
- Multipartite entanglement in spin chains
- Quantum inseparability as local pseudomixture
- Genuine 12-qubit entanglement on a superconducting quantum processor
- Distillability Criterion for all Bipartite Gaussian States
- Separability Criterion for all bipartite Gaussian States
- Entanglement Witnesses in Spin Models
- Characterization of separable states and entanglement witnesses
- Generalized Gibbs Ensembles for Quantum Field Theories
- Long range correlations in the non-equilibrium quantum relaxation of a spin chain
- Quantum quenches in a spinor condensate
- Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
- Exploring local quantum many-body relaxation by atoms in optical superlattices
- Quantum Quench from a Thermal Initial State
- Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
- On the partial transpose of fermionic Gaussian states
- Energy as an Entanglement Witness for Quantum Many-Body Systems
- Failure of the GGE hypothesis for integrable models with bound states
- Scaling of genuine multiparticle entanglement at a quantum phase transition
- Entanglement negativity bounds for fermionic Gaussian states
- Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
- Negative eigenvalues of partial transposition of arbitrary bipartite states
- Entanglement Observables and Witnesses for Interacting Quantum Spin Systems
- Quantum relaxation and finite size effects in the XY chain in a transverse field after global quenches
- Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
- Integrability vs Quantum Thermalization
- Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
- Energy and multipartite entanglement in multidimensional and frustrated spin models
- Genuine Multipartite Entanglement in the Model
- Thermal entanglement in the nanotubular system Na_2V_3O_7
- Memory of the Initial Conditions in an Incompletely-Chaotic Quantum System: Universal Predictions and an Application to Cold Atoms
- Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments
- Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
- An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
- Bound entanglement in the XY model
- Detection of multipartite entanglement with two-body correlations
- Energy as witness of multipartite entanglement in spin clusters
- Towards the chemical tuning of entanglement in molecular nanomagnets
- Detection of entanglement between collective spins
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- Quantum chaos in a harmonic waveguide with scatterers
- Entanglement signatures of a percolating quantum system
- Nonequilibrium tricritical behaviour in anisotropic XY ferromagnet driven by elliptically polarised propagating magnetic field wave
- Threetangle in the XY-model class with a non-integrable field background