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Modern Physics Letters A

Thermal quantum correlations in a two-dimensional spin star model

Saeed Haddadi, Mohammad Reza Pourkarimi, Ahmad Akhound, Mehrdad Ghominejad

Published May 27, 2019• 32 citations
Publisher

Abstract

In this paper, we study the thermal evolution of three types of quantum correlations under the homogeneous and inhomogeneous spin star Hamiltonian. It is shown that quantum discord (QD) is more stable than the other measures in the thermal regime, but concurrence is more efficient when the Hamiltonian parameters are employed. However, all quantum correlations can reach their maximum, if the inhomogeneous parameter raises. Quantum correlations can be enhanced by a weak external magnetic field and strong coupling parameter. But they vanish in the case of a strong magnetic field, weak coupling parameter, and high temperatures.

DOI
10.1142/s021773231950175x

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In this paper, we study the thermal evolution of three types of quantum correlations under the homogeneous and inhomogeneous spin star Hamiltonian. It is shown that quantum discord (QD) is more stable than the other measures in the thermal regime, but concurrence is more efficient when the Hamiltonian parameters are employed. However, all quantum correlations can reach their maximum, if the inhomogeneous parameter raises. Quantum correlations can be enhanced by a weak external magnetic field and strong coupling parameter. But they vanish in the case of a strong magnetic field, weak coupling parameter, and high temperatures.
We study the influences of the external magnetic field, temperature, and coupling parameter on the thermal quantum correlation in a two-qubit Heisenberg XY model, where the correlation is described in terms of two modified geometric discords and concurrence. It is shown that those three quantities behave similarly in the regions of lower temperature and weak magnetic field. However, the two geometric discords are more robust against temperature and magnetic field than the concurrence. Moreover, two geometric discords exhibit different behaviors under suitable conditions, that is, one discord increases as the magnetic field rises whereas the other discord decreases. In particular, the discord reveals the phenomenon of sudden change, while neither of other discord and concurrence displays such a phenomenon.
In contrast with the thermal entanglement, we study the quantum discord and classical correlation in a two-qubit Heisenberg XXZ model with an inhomogeneous magnetic field. It is shown that the effects of the external magnetic fields, including the uniform and inhomogeneous magnetic fields, on the thermal entanglement, quantum discord and classical correlation behave differently in various aspects, which depend on system temperature and model type. We can tune the inhomogeneous magnetic field to enhance the entanglement or classical correlation and meanwhile decrease the quantum discord. In addition, taking into account the inhomogeneous magnetic field, the sudden change in the behaviour of quantum discord still survives, which can detect the critical points of quantum phase transitions at finite temperature, but not for a uniform magnetic field.
We investigate the quantum discord in the thermal states for a spin-star model consisting of three parties which include one central spin and the other two outer spins. Our results imply that the quantum correlation can be established between the two outer spins both of which interacting with the central spin independently. From the analysis, we find that the quantum discord and entanglement depends not only on the external magnetic field and the interaction strength but also on the anisotropy parameter and the temperature. Specially, the quantum discord is more robust than the quantum entanglement in the sense that the quantum discord lasts for higher temperatures than the entanglement does.
Abstract The thermal quantum correlations in a two-qubit one-dimensional XXZ Heisenberg spin- 1 2 chain subjected to an inhomogeneous magnetic field are investigated. The concurrence, as thermal entanglement quantifier, and the discord-like quantifiers, namely the trace distance discord and local quantum uncertainty, are computed. Their dependence on the anisotropy parameter γ , uniform magnetic field B , coupling constant J and nonuniform magnetic field b are presented in detail. The mentioned quantifiers behaviors in terms of this parameters are compared and discussed. The results show that TDD is always much stronger than the concurrence and LQU, whereas the latter two show a swinging behavior depending on system parameters. Also, we have shown that the nonuniform magnetic field can reduce the effects of temperature on thermal correlations. Furthermore, the thermal correlations, for fixed values of b , can be enhanced in the antiferromagnetic system in comparison to the ferromagnetic one. In addition, the quantum correlations amounts in the ferromagnetic system are deteriorated when γ decreases, but they are improved when the system is antiferromagnetic.
The thermal quantum discord (QD) is investigated in the two-qubit anisotropic Heisenberg XXZ model under an external non-uniform magnetic field along the Z-axis. We obtain the analytical expressions of the thermal QD and thermal entanglement measured by concurrence (C). It shows that for any temperature T, QD gradually decreases with the increase of non-uniform magnetic field |b|, in some regions where C increases while QD decreases. It is also found that thermal quantum discord does not vanish at finite temperatures, but concurrence vanishes completely at a critical temperature. It is shown that for a higher value of JZ, the system has a stronger QD. There is a critical magnetic field B c , which increases with the increasing b. QD decay monotonically (for B < B c ) when temperature T increases, or initially increases to some peaks and then decrease (for B > B c ).