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International Journal of Recent advances in Physics

Thermal Entanglement of a Qubitqutrit Chain

Safa Jami, Z. Amerian

Published May 31, 2014• 2 citations
Publisher

Abstract

In this paper we study the effect of temperature, magnetic field, and exchange coupling on the thermal entanglement in a spin chain which consist of two qubits and one qutrit.We use negativity as a measure of entanglement in our study.We apply magnetic field, uniform and nonuniform field, on it.The results show that the entanglement decreases with increase in temperature.Also, we have found that under a magnetic field, either uniform or nonuniform, in constant temperature, the entanglement decreases.We have found that increasing exchange coupling of any two particles decreases the entanglement of the other two particles.Finally, we have compared our system with a two-particle system and found that in presence of a magnetic field the increase in number of particles leads to the decrease in the entanglement.

DOI
10.14810/ijrap.2014.3206

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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 .
We investigate the impurity entanglement of 3-qutrit XXX-type Heisenberg chains in the presence of a uniform magnetic field along z axis by means of negativity. The entanglement is calculated as a function of the coupling constants J, impurity parameter J1, magnetic fields B and temperature T. Through calculating the negativity between sites 1 and (2,3) N1-23 and sites 3 and (1,2) N12-3, we show that the critical temperature Tc above which the entanglement vanishes increases with the increase of J1. The existence of magnetic fields B can obviously reduce the entanglement, and it is found that the limiting temperature Tc depends on the impurity parameter J1 but not on the magnetic field.
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We study the entanglement of a two-qubit one-dimensional XYZ Heisenberg chain in thermal equilibrium at temperature T. We obtain an analytical expression for the concurrence of this system in terms of the parameters of the Hamiltonian and T. We show that depending on the relation among the coupling constants, it is possible to increase the amount of entanglement of the system by increasing its anisotropy. We also show numerically that for all sets of the coupling constants entanglement is a monotonically decreasing function of the temperature T, proving that we must have at least an external magnetic field in the z-direction to obtain a behavior where entanglement increases with T.