Thermal entanglement properties of small spin clusters

Abstract

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. In this paper, we consider a spin tetramer, with spins of magnitude 1/2, in which the spins interact via nearest-neighbour, diagonal and four-spin interactions of strength J1, J2 and K respectively. The ground and thermal state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Signatures of quantum phase transition (QPT) in terms of appropriate entanglement measures are obtained. The magnetic properties of a S = 1/2 AFM polyoxovanadate compound, V12, are well explained by spin tetramers with only nearest-neighbour exchange interactions. Treating the magnetic susceptibility chi as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature, T_c, above which the multipartite entanglement disappears in the experimental compound, is determined. A second EW based on energy provides an estimate of the entanglement temperature T_E, below which bipartite entanglement is certainly present in the system, is determined. The cases of the symmetric trimer and the tetrahedron are also considered.

20 pages, 10 figures

References in corpus (38)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum Computation with Quantum Dots
• Entanglement in quantum critical phenomena
• Distributed Entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Coupled quantum dots as quantum gates
• Entanglement in a simple quantum phase transition
• Universal Quantum Computation with the Exchange Interaction
• Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
• Entanglement in the Quantum Heisenberg XY model
• Quantum Phase Transitions and Bipartite Entanglement
• Entanglement versus Correlations in Spin Systems
• Violation of local uncertainty relations as a signature of entanglement
• Entangled Rings
• Entangled Quantum States of Magnetic Dipoles
• Entanglement in a second order quantum phase transition
• Thermal concurrence mixing in a 1D Ising model
• Localizable Entanglement
• Implementation of Spin Hamiltonians in Optical Lattices
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Quantum entanglement and Bell inequalities in Heisenberg spin chains
• Effects of anisotropy on thermal entanglement
• Entanglement Witnesses in Spin Models
• 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
• Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model
• Global entanglement and quantum criticality in spin chains
• Thermal entanglement in three-qubit Heisenberg models
• Nature and Measure of Entanglement in Quantum Phase Transitions
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Entanglement and correlation in anisotropic quantum spin systems
• Macroscopic entanglement jumps in model spin systems
• Neutron Scattering and Magnetic Observables for S = 1/2 Molecular Magnets
• The entanglement of Heisenberg chain with next-nearest-neighbor interaction
• Entanglement and Quantum Phases in the Anisotropic Ferromagnetic Heisenberg Chain in the Presence of Domain Walls
• Three and Four-Body Interactions in Spin-Based Quantum Computers
• Mean Field Approximations and Multipartite Thermal Correlations

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• Quantum Discord in the Ground and Thermal States of Spin Clusters
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• Entanglement in thermal equilibrium states
• Thermal entanglement between non-nearest-neighbor spins on fractal lattices
• Thermal entanglement witness for materials with variable local spin lengths
• Thermal entanglement of spins in mean-field clusters
• Entanglement in a molecular three-qubit system
• Quantum Information Resources in Spin-1 Heisenberg Dimer Systems
• Control of entanglement transitions in quantum spin clusters
• Thermal entanglement of qubit pairs on the Shastry-Sutherland lattice
• Experimental Evidences of Quantum Phase Transition in a Spin Cluster Compound
• Dynamic generation of entangling wave packets in XY spin system with decaying long range couplings
• Entanglement of the Ising-Heisenberg diamond spin-1/2 cluster in evolution
• Thermally stable multipartite entanglements in the frustrated Heisenberg hexagon
• Entanglement in Anderson Nanoclusters
• Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
• Spin-1/2 $XXZ$ Heisenberg cupolae: magnetization process and related enhanced magnetocaloric effect
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Spin-interactions in Mineral Libethenite Series: Evolution of Low-dimensional Magnetism
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