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Journal of the Korean Physical Society

Magnetic Field Effects on Quantum Correlations for the XXX Heisenberg Spin Chain

Safa Jami, Zohreh Haqpanah

Published Apr 1, 2018• 3 citations

Abstract

We study the geometric quantum discord (GQD) for three spin 1/2 particles in the XXX Heisenberg model with an external magnetic field. We investigate the effect of temperature and J (the strength of interaction) on the GQD. Then, we apply a uniform magnetic field to our system and study the behavior of the GQD under the field. Furthermore, we compare the behavior of the GQD to the entanglement for our system under the above parameters.

DOI: 10.3938/jkps.72.743

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We study the geometric quantum discord (GQD) for three spin 1/2 particles in the XXX Heisenberg model with an external magnetic field. We investigate the effect of temperature and J (the strength of interaction) on the GQD. Then, we apply a uniform magnetic field to our system and study the behavior of the GQD under the field. Furthermore, we compare the behavior of the GQD to the entanglement for our system under the above parameters.

In this paper we argue about the quantum correlation (quantum entanglement and geometric quantum discord) in four-qubit XXZ Heisenberg Model. Here, the influence of uniform magnetic field on the dynamics of quantum correlation in cases of the antiferromagnetism has been mainly investigated. According to the results, it has been illustrated that the role of the uniform magnetic field on the dynamics of quantum correlation depends on the selection of the initial state. Furthermore, geometric quantum discord exhibits greater robustness compared to quantum entanglement. Also results show that the max values of quantum correlations decrease and the duration of quantum entanglement sudden death gets longer as purity parameter decreases, and that exchange interaction can substantially make an effect on the dynamics of the quantum correlation.

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.

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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.