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Physical Review B

Magnetic field effect on the macroscopic thermal entanglement of a dimerized chain of qubits

Andrei A. Zvyagin

Published Dec 22, 2011• 3 citations
Publisher

Abstract

The effect of dimerization on the macroscopic tangle and thermal pairwise entanglement for a system of coupled qubits with interactions is studied. The exactly solvable model permits us to obtain analytic formulas for characteristics of the macroscopic thermal entanglement. Two special cases of the dimerization are considered: the dimerization of couplings, and the dimerization of level spacings of nearest-neighbor qubits in the chain. In the first case the dimerization of couplings essentially affects the thermal entanglement. On the other hand, the dimerization of the level spacings for qubits in the chain produces only quantitative changes in the macroscopic thermal entanglement compared to the homogeneous case.

DOI
10.1103/physrevb.84.214431

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The effect of dimerization on the macroscopic tangle and thermal pairwise entanglement for a system of coupled qubits with interactions is studied. The exactly solvable model permits us to obtain analytic formulas for characteristics of the macroscopic thermal entanglement. Two special cases of the dimerization are considered: the dimerization of couplings, and the dimerization of level spacings of nearest-neighbor qubits in the chain. In the first case the dimerization of couplings essentially affects the thermal entanglement. On the other hand, the dimerization of the level spacings for qubits in the chain produces only quantitative changes in the macroscopic thermal entanglement compared to the homogeneous case.
In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.
We examine the entanglement of thermal states of nnn spins interacting through different types of XYXYXY couplings in the presence of a uniform magnetic field, by evaluating the negativities of all possible bipartite partitions of the whole system and of subsystems. We consider both the case where every qubit interacts with all others and where just nearest neighbors interact in a one-dimensional chain. Limit temperatures for nonzero negativities are also evaluated and compared with the mean field critical temperature. It is shown that limit temperatures of global negativities are strictly independent of the magnetic field in all XXZXXZXXZ models, in spite of the quantum transitions that these models may exhibit at zero temperature, while in anisotropic models they always increase for sufficiently large fields. Results also show that these temperatures are higher than those limiting pairwise entanglement.
The thermal entanglement in the Heisenberg XYZ\mathrm{XYZ}XYZ chain is investigated in the presence of an external magnetic field B. In the two-qubit system, the critical magnetic field Bc{B}_{c}Bc​ is increased by introducing the interaction of the z component of two neighboring spins Jz.{J}_{z}.Jz​. This interaction not only improves the critical temperature Tc,{T}_{c},Tc​, but also enhances the entanglement for a particular fixed B. We also analyze the pairwise entanglement between nearest neighbors in three qubits. The pairwise entanglement, for a fixed T, can become strong by controlling B and Jz.{J}_{z}.Jz​.
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We elucidate the finite temperature entanglement properties of N=9N=9N=9 qubits Heisenberg XXXXXX and XXZXXZXXZ models under the presence of a polarized magnetic field in xzxzxz plane by means of concurrence concept. We perform a systematic analysis for a wide range of the system parameters. Our results suggest that the global phase regions which separate the entangled and non-entangled regions sensitively depend upon the spin-spin interaction term of the z−z-z− component of two neighboring spins Jz/JxJ_{z}/J_{x}Jz​/Jx​, temperature as well as polarized magnetic field components. Thereby, we think that polarized magnetic field can be used a control parameter to determine the amount of thermal entanglement between pair of qubits for different temperatures and spin-spin interaction terms. Moreover, it has been found that the nearest-neighbor pair of qubits does not point out a re-entrant type entanglement character when one only deals with the nearest-neighbor pair of qubits. However, as one considers next-nearest neighbor pair of qubits, it is possible to see the evidences of re-entrant type entanglement behaviors.