Entanglement and correlation in anisotropic quantum spin systems

Abstract

Analytical expressions for the entanglement measures concurrence, i-concurrence and 3-tangle in terms of spin correlation functions are derived using general symmetries of the quantum spin system. These relations are exploited for the one-dimensional XXZ-model, in particular the concurrence and the critical temperature for disentanglement are calculated for finite systems with up to six qubits. A recent NMR quantum error correction experiment is analyzed within the framework of the proposed theoretical approach.

8 pages, 3 figures

References in corpus (21)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement of a Pair of Quantum Bits
• Entanglement in quantum critical phenomena
• Distributed Entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Universal state inversion and concurrence in arbitrary dimensions
• Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
• Global entanglement in multiparticle systems
• Entangled Rings
• Thermal concurrence mixing in a 1D Ising model
• Quantum computing with spin cluster qubits
• Quantum entanglement and Bell inequalities in Heisenberg spin chains
• Implementation of the Five Qubit Error Correction Benchmark
• Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model
• Thermal entanglement in three-qubit Heisenberg models
• The Importance of being Odd
• Macroscopic entanglement jumps in model spin systems
• Entanglement in quantum computers described by the XXZ model with defects
• Entanglement in SU(2)-invariant quantum spin systems
• Violation of Bell inequality for thermal states of interaction qubits via a multi-qubit Heisenberg model

Cited by in corpus (50)

• Fidelity approach to quantum phase transitions
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Quantum discord and its allies: a review
• Entanglement in a first order quantum phase transition
• Entanglement and Quantum Phase Transition Revisited
• Entanglement dynamics in the Lipkin-Meshkov-Glick model
• Nature and Measure of Entanglement in Quantum Phase Transitions
• Density matrix quantum Monte Carlo
• Coherent and dissipative dynamics at quantum phase transitions
• Entanglement Observables and Witnesses for Interacting Quantum Spin Systems
• Entanglement Across a Transition to Quantum Chaos
• Entanglement of electron spins of non-interacting electron gases
• Thermal Entanglement between Alternate Qubits of a Four-qubit Heisenberg XX Chain in a Magnetic Field
• Probability density function characterization of multipartite entanglement
• Thermal entanglement properties of small spin clusters
• The Wavefunction of an Anyon
• Thermally activated Peierls dimerization in ferromagnetic spin chains
• Boundary and impurity effects on entanglement of Heisenberg chains
• Entanglement and Quantum Phases in the Anisotropic Ferromagnetic Heisenberg Chain in the Presence of Domain Walls
• Entanglement in spin-one Heisenberg chains
• Reading entanglement in terms of spin configurations in quantum magnets
• Global entanglement in XXZ chains
• Quantum teleportation via a two-qubit Heisenberg XXZ chain-effects of anisotropy and magnetic field
• Magnetic quantum correlation in the 1D transverse-field XXZ model
• Global thermal entanglement in n-qubit systems
• Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: global thermodynamics from renormalization group theory
• Spin-1/2 Heisenberg ladder: variation of entanglement and fidelity measures close to quantum critical points
• Characterization of entanglement of more than two qubits with Bell inequalities and global entanglement
• Strongly entangled light from planar microcavities
• Entanglement in thermal equilibrium states
• Entangled spin clusters: some special features
• Thermal entanglement between non-nearest-neighbor spins on fractal lattices
• Analytical results for entanglement in the five-qubit anisotropic Heisenberg model
• Mode entanglement of an electron in one-dimensional determined and random potentials
• Entanglement and quantum phase transition in quantum mixed spin chains
• Swapping and permutation operators as entanglement witnesses for quantum Heisenberg spin-$s$ systems
• Effects of anisotropy on optimal dense coding
• Entanglement in spin-1/2 dimerized Heisenberg systems
• Local entanglement and String Order Parameter in dimerized models
• Entanglement and coherence in a spin-s XXZ system under non-uniform fields
• Ground-state properties of the two-site Hubbard-Holstein model: an exact solution
• Thermally stable multipartite entanglements in the frustrated Heisenberg hexagon
• Entanglement in the Bogoliubov vacuum
• Entanglement oscillations in open Heisenberg chains
• Effect of three-spin interaction on thermal entanglement in Heisenberg XXZ model
• Logarithmic negativity of the 1D antiferromagnetic spin-1 Heisenberg model with single-ion anisotropy
• Quantum Separability of Thermal Spin One Boson Systems
• Witnessing Disorder in Quantum Magnets
• Spin Squeezing, Macrorealism and the Heisenberg uncertainty principle
• Non-local spin entanglement in a fermionic chain