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Chinese Physics Letters

Thermal Entanglement in Spin-Dimer V 4+ with a Strong Magnetic Field

Zhang Guo-Feng, Liang Jiu-Qing, Qiwei Yan

Published Mar 26, 2003• 14 citations
Publisher

Abstract

We study the entanglement in Heisenberg dimer single molecular magnets V 4+ with a strong magnetic field by means of the measure of entanglement called ``concurrence'' and find that thermal entanglement exists for both the ferromagnetic (FM) and antiferromagnetic (AFM) cases. In the FM case, entanglement vanishes for anisotropic parameter λ = 0 while in the AFM case, entanglement exits in the whole region of anisotropic parameter 0⩽λ⩽1. Entanglement variations with anisotropic parameter λ, magnetic field B and temperature T are evaluated. We find a critical magnetic field at which the concurrence changes sharply from zero to maximum entanglement.

DOI
10.1088/0256-307x/20/4/303

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We study the entanglement in Heisenberg dimer single molecular magnets V 4+ with a strong magnetic field by means of the measure of entanglement called ``concurrence'' and find that thermal entanglement exists for both the ferromagnetic (FM) and antiferromagnetic (AFM) cases. In the FM case, entanglement vanishes for anisotropic parameter λ = 0 while in the AFM case, entanglement exits in the whole region of anisotropic parameter 0⩽λ⩽1. Entanglement variations with anisotropic parameter λ, magnetic field B and temperature T are evaluated. We find a critical magnetic field at which the concurrence changes sharply from zero to maximum entanglement.
By means of the measure of entanglement called "concurrence" we study the entanglement in Heisenberg dimer single molecular magnets V4+ with a strong magnetic field and find that thermal entanglement exits for both ferromagnetic (FM) and antiferromagnetic (AFM) cases. In FM case entanglement vanishes for anisotropic parameter λ = 0 while in AFM case, entanglement exits in the whole region of anisotropic parameter 0 ≤ λ ≤ 1. Entanglement variations with anisotropic parameter λ, magnetic field B and temperature T are evaluated. We find a critical magnetic field at which the concurrence changes sharply from zero to maximum entanglement.
The thermal entanglement in spin-dimer V4+ model under an uniform magnetic field is analyzed,and it is found that thermal entanglement exits for both ferromagnetic and antiferromagnetic cases.In antiferromagnetic case,entanglement vanishes for anisotropic parameter value λ=0,while in ferromagnetic case,entanglement exits in the whole region of anisotropic parameter 0≤λ≤1.Concurrence variations with anisotropic parameter λ,magnetic field and temperature are evaluated.It is useful for solid-quantum calculation in future.
We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .
We have investigated the properties of thermal entanglement in a triangular spin ring of the single molecular magnet (SMM) Na9[Cu3Na3(H2O)9 (α-AsW9O33)2]·26H2O in a magnetic field, and the pairwise concurrences of arbitrary two Cu2+ ion qubits are calculated numerically, hereafter abbreviated as C12, C23 and C13, respectively. Results show that the magnitude and direction of magnetic field as well as temperature have important effects on the pairwise thermal entanglement. Moreover, C12, C23 and C13 have difference variations with the change of the parameters. We also plot the changes of the critical temperatures Tc of C12, C23 and C13 with the magnetic fields along three different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the ranges of parameters in which the pairwise thermal entanglement in a triangular spin ring of the SMM exists. Therefore, the pairwise entanglement can be controlled and enhanced in the SMM by choosing appropriate magnitude and direction of magnetic field and temperature.
We numerically investigate thermal entanglement of the spins (1/2,1) and (1/2,1/2) in the three-mixed (1/2,1,1/2) anisotropic Heisenberg XXZ spin system on a simple triangular cell under an inhomogeneous magnetic field. We show that the external magnetic field induces strong plateau formation in pairwise thermal entanglement for fixed parameters of Hamiltonian in the case of the ferromagnetic and anti-ferromagnetic interactions. We also observe an unexpected critical point at finite temperature in the thermal entanglement of the spins (1/2,1) for antiferromagnetic case while the entanglement of the spins (1/2,1) for ferromagnetic case and the entanglement of the spins (1/2,1/2) for both ferromagnetic and antiferromagnetic cases almost decays exponentially to zero with increasing temperature. The critical point in entanglement of the spins (1/2,1) for antiferromagnetic case may be signature of the quantum phase transition at finite temperature.