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Journal of Physical & Theoretical Chemistry

Thermal negativity in a two qubit XXX and XX spin chain model in an external magnetic field

M Ghasemloo, N Nikdel, Mohammad Reza Soltani, M Firoozi, F. Soheilian

Published Jul 1, 2013• 1 citation

Abstract

In this paper we studied the thermal negativity in a two-qubit XX spin ½ chain model and XXX spin 1/2 chain model(isotropic Heisenberg model)spin-1/2 chain subjected to an external magnetic field in z direction. We calculate analytical relation for the thermal negativity for two qubit XX and XXX spin chain models in the external magnetic field. Effects of the magnetic field and temperature on the negativity are shown. We have also plotted two kind of behavior in the thermal negativity which scales by magnetic field and temperature. It is shown that when the magnetic field along in axis z is considerable, thermal negativity can be decrease for higher temperature. We found the critical temperature of negativity for XX spin chain model and XXX spin chain model with added external magnetic field where there are independent from magnetic field. We also have shown in both of two models after T=TC the negativity is zero. We find the critical temperature for this models and show that the critical temperature is independent of magnetic field. We found that the negativity with increasing the temperature T, at first the quantum correlations in the system increase, smoothly reaches the maximum, and then after the critical temperature turn into zero.

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In this paper we studied the thermal negativity in a two-qubit XX spin ½ chain model and XXX spin 1/2 chain model(isotropic Heisenberg model)spin-1/2 chain subjected to an external magnetic field in z direction. We calculate analytical relation for the thermal negativity for two qubit XX and XXX spin chain models in the external magnetic field. Effects of the magnetic field and temperature on the negativity are shown. We have also plotted two kind of behavior in the thermal negativity which scales by magnetic field and temperature. It is shown that when the magnetic field along in axis z is considerable, thermal negativity can be decrease for higher temperature. We found the critical temperature of negativity for XX spin chain model and XXX spin chain model with added external magnetic field where there are independent from magnetic field. We also have shown in both of two models after T=TC the negativity is zero. We find the critical temperature for this models and show that the critical temperature is independent of magnetic field. We found that the negativity with increasing the temperature T, at first the quantum correlations in the system increase, smoothly reaches the maximum, and then after the critical temperature turn into zero.

Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.

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.

The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field ( B ), a parameter b which controls the inhomogeneity of B , and the bilinear interaction parameters J x = J y ≠ J z on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of J z and lower values of B and b .

In this paper, the entanglement in a spin-1 Heisenberg XXZ chain with uniform and nonuniform external magnetic field is investigated in the terms of the measure of entanglement called 'negativity'. The effects of the external magnetic field, the anisotropy parameter and the temperature on the negativity are discussed respectively. It can be seen that the entanglement in this spin chain for any temperature is symmetric with respect to zero magnetic field. We calculate the partially transposed density matrix and give qualitatively results at different temperatures. In order to show the results clearly, the behavior of negativity is presented for five different cases. It can be found that the temperature and the external magnetic field can effect the feature of the thermal entanglement significantly. In addition, under certain condition, the negativity may be enhanced under a nonuniform magnetic field.

The entanglement at zero-temperature is studied in a two-qubit XZ spin-1/2 chain model in an external magnetic field which is applied in the z direction. We have obtained an analytical relation for the effect of the external magnetic field on the concurrence. It is shown that the ground state of the system depends on the strength of exchange coupling. We have shown that the analytical relation of the concurrence is independent of Jz. It is shown that for Jz >0 the concurrence is depended on the critical value of the external magnetic field and it is changed at the critical external magnetic field. Also we have shown that for h hc, the concurrence decreases by increasing the external magnetic field. For Jz <0, the concurrence decreases by increasing the external magnetic field.

Negativity is an universal entanglement measure.The entanglement of two-party quantum system can be easily calculated with negativity.The thermal entanglement in the two qubit anisotropic Heisenberg XXZ model is studies by means of Negativity.The influence of temperature T and an external magnetic field B on the entanglement is investigated in thermal equilibrium.When the temperature is less than an critical temperature TC,the thermal entanglement is depended on the magnetic field strength,otherwise the entanglement disappears.