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International Journal of Modern Physics B

THERMAL ENTANGLEMENT IN SPIN SYSTEMS

N. Canosa, R. Rossignoli

Published Dec 15, 2006• 1 citation
Publisher

Abstract

We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.

DOI
10.1142/s021797920603617x

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We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.
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.
We examine the thermal entanglement of XXZXXZXXZ-type Heisenberg chains in the presence of a uniform magnetic field along the zzz axes through the evaluation of the negativity associated with bipartitions of the whole system and subsystems. Limit temperatures for nonzero global negativities are shown to depend on the asymmetry $\ensuremath{\Delta}$, but not on the uniform field, and can be much higher than those limiting pairwise entanglement. It is also shown that global bipartite entanglement may exist for T>0T>0T>0 even for $\ensuremath{\Delta}\ensuremath{\geqslant}1$, i.e., when the system is fully aligned (and hence separable) at T=0T=0T=0, and that the bipartition leading to the highest limit temperature depends on $\ensuremath{\Delta}$.
The effects of spin-spin interaction on thermal entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the J i (i-axis spin-spin interaction), the higher critical value the B i (i-axis uniform magnetic field) has. Moreover, in the weak-field regime, the larger J i corresponds to more entanglement, while in the strong-field regime, different J i correspond to the same entanglement. In addition, it is found that with the increase of J i , the concurrence can approach the maximum value more rapidly for the smaller B i , and can reach a larger value for the smaller b i (i-axis nonuniform magnetic field). So we can get more entanglement by increasing the spin-spin interaction J i , or by decreasing the uniform magnetic field B i and the nonuniform magnetic field b i .
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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.
We examine the entanglement of general mixed states of a two-qubit Heisenberg XYZXYZXYZ chain in the presence of a magnetic field, and its detection by means of different criteria. Both the exact separability conditions and the weaker conditions implied by the disorder and the von Neumann entropic criteria are analyzed. The ensuing limit temperatures for entanglement in thermal states of different XYZXYZXYZ models are then examined and compared with the limit temperature of the symmetry-breaking solution in a mean-field-type approximation. The latter, though generally lower, can also be higher than the exact limit temperature for entanglement in certain cases, indicating that symmetry breaking does not necessarily entail entanglement. The reentry of entanglement for increasing temperatures is also discussed.