Entanglement and Quantum Phase Transition Revisited

Abstract

We show that, for an exactly solvable quantum spin model, a discontinuity in the first derivative of the ground state concurrence appears in the absence of quantum phase transition. It is opposed to the popular belief that the non-analyticity property of entanglement (ground state concurrence) can be used to determine quantum phase transitions. We further point out that the analyticity property of the ground state concurrence in general can be more intricate than that of the ground state energy. Thus there is no one-to-one correspondence between quantum phase transitions and the non-analyticity property of the concurrence. Moreover, we show that the von Neumann entropy, as another measure of entanglement, can not reveal quantum phase transition in the present model. Therefore, in order to link with quantum phase transitions, some other measures of entanglement are needed.

RevTeX 4, 4 pages, 1 EPS figures. some modifications in the text. Submitted to Phys. Rev. A

References in corpus (20)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Quantum Phase Transitions and Bipartite Entanglement
• Entanglement and the Phase Transition in Single Mode Superradiance
• Entanglement versus Correlations in Spin Systems
• Entanglement and quantum phase transition in the extended Hubbard model
• Local entanglement and quantum phase transition in the Hubbard model
• Entangled Rings
• Entanglement in a second order quantum phase transition
• Entanglement, quantum phase transition and scaling in XXZ chain
• Quantum entanglement and Bell inequalities in Heisenberg spin chains
• Thermal and ground-state entanglement in Heisenberg XX qubit rings
• Studying quantum spin systems through entanglement estimators
• Entanglement in a first order quantum phase transition
• Entanglement and Spontaneous Symmetry Breaking in Quantum Spin Models
• Entanglement and correlation in anisotropic quantum spin systems
• Macroscopic entanglement jumps in model spin systems
• Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets

Cited by in corpus (78)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Classical Correlation and Quantum Discord in Critical Systems
• Quantum coherence and uncertainty in the anisotropic XY chain
• Quantum discord and its allies: a review
• Genuine quantum correlations in quantum many-body systems: a review of recent progress
• Two-site entropy and quantum phase transitions in low-dimensional models
• Global entanglement and quantum criticality in spin chains
• Quantum Correlations and Coherence in Spin-1 Heisenberg Chains
• Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems
• Linking entanglement and quantum phase transitions via density functional theory
• The ground state entanglement in the $XXZ$ model
• A generalized skew information and uncertainty relation
• An elementary formula for entanglement entropies of fermionic systems
• Bell inequalities and entanglement at quantum phase transition in the XXZ Model
• Block-block entanglement and quantum phase transitions in one-dimensional extended Hubbard model
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases
• Quantum Entanglement in the Two Impurity Kondo Model
• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Local Entanglement and quantum phase transition in spin models
• Genuine Multipartite Entanglement Trends in Gapless-gapped Transitions of Quantum Spin Systems
• Dynamical phase transitions and temperature induced quantum correlations in an infinite spin chain
• Entanglement induced in spin-1/2 particles by a spin chain near its critical points
• Dynamic properties of the spin-1/2 XY chain with three-site interactions
• Quantum discord in the ground state of spin chains
• XY model on the circle: diagonalization, spectrum, and forerunners of the quantum phase transition
• Multipartite Entanglement Accumulation in Quantum States: Localizable Generalized Geometric Measure
• Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model
• Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model
• Quantum information analysis of the phase diagram of the half-filled extended Hubbard model
• Entanglement patterns and generalized correlation functions in quantum many body systems
• Dynamical topological quantum phase transitions in nonintegrable models
• Parity quantum numbers in the Density Matrix Renormalization Group
• Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
• Characterizing entanglement by momentum-jump in the frustrated Heisenberg ring at quantum phase transition
• Quantum State Transfer Characterized by Mode Entanglement
• Speedup of quantum state transfer by three- qubit interactions: Implementation by nuclear magnetic resonance
• Spatially nonuniform phases in the one-dimensional SU(n) Hubbard model for commensurate fillings
• Interplay between quantum phase transitions and the behavior of quantum correlations at finite temperatures
• Multi-partite quantum nonlocality and Bell-type inequalities in an infinite-order quantum phase transition of the one-dimensional spin-1/2 XXZ chain
• Geometric Phase and Quantum Phase Transition in the Lipkin-Meshkov-Glick model
• Comb entanglement in quantum spin chains
• Entanglement and quantum phase transitions
• Unified phase diagram of models exhibiting neutral-ionic transition
• Static and dynamical quantum correlations in phases of an alternating field XY model
• Finite Size Corrections to Entanglement in Quantum Critical Systems
• Entanglement and magnetic order
• Probing the quantum phase transition in the Dicke model through mechanical vibrations
• Quantum Entanglement and fixed point Hopf bifurcation
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Phase boundaries in alternating field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics
• Density Matrix Recursion Method: Genuine Multisite Entanglement Distinguishes Odd from Even Quantum Heisenberg Ladders
• Entanglement scaling at first order phase transitions
• Characterization of a correlated topological Kondo insulator in one dimension
• Detecting phase boundaries of quantum spin-1/2 XXZ ladder via bipartite and multipartite entanglement transitions
• Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems
• Genuine tripartite entanglement monotone of $(2\otimes 2\otimes n)-$ dimensional systems
• Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpiński fractal lattices
• Bell-CHSH function approach to quantum phase transitions in matrix product systems
• Partial entropy in finite-temperature phase transitions
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization
• General Quantum State Swap: an XY model analysis
• Enhancement of non-equilibrium thermal quantum discord and entanglement of a three-spin XX chain by multi-spin interaction and external magnetic field
• Quantum phase transition and entanglement in Li atom system
• Interorbital interaction in the one-dimensional periodic Anderson model: A density-matrix renormalization-group study
• Entanglement and dynamical phase transition in a spin-orbit-coupled Bose-Einstein condensate
• Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
• Competition between Hund's coupling and Kondo effect in a one-dimensional extended periodic Anderson model
• Effect of three-spin interaction on thermal entanglement in Heisenberg XXZ model
• Odd-even effect of quantum discord and quantum phase transitions in the S=1/2 spin ladder with ring exchange
• Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Ground State Instabilities and Entanglement in the Detuned Dicke Model
• Entanglement and Quantum Phase Transitions via Adiabatic Quantum Computation
• Designing lattice structures with maximal nearest-neighbor entanglement
• Detecting entanglement with transport measurement in weakly interacting and fluctuating systems