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arXiv:1604.02655 · International Journal of Modern Physics B

Nonlocal correlation in Heisenberg spin models

R. Muthuganesan, R. Sankaranarayanan

Published May 9, 2017• 6 citations
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Abstract

In this paper, we investigate nonlocal correlation (beyond entanglement) captured by measurement induced nonlocality and geometric quantum discord for a pair of interacting spin-1/2 particles at thermal equilibrium. It is shown that both the measures are identical in measuring the correlation. We show that nonlocal correlation between the spins exist even without entanglement and the correlation vanishes only for maximal mixture of product bases. We also observe that while interaction between the spins is responsible for enhancement of correlation, this non-classicality decreases with the intervention of external magnetic field.

DOI
10.1142/s0217979217501661

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In this paper, we investigate nonlocal correlation (beyond entanglement) captured by measurement induced nonlocality and geometric quantum discord for a pair of interacting spin-1/2 particles at thermal equilibrium. It is shown that both the measures are identical in measuring the correlation. We show that nonlocal correlation between the spins exist even without entanglement and the correlation vanishes only for maximal mixture of product bases. We also observe that while interaction between the spins is responsible for enhancement of correlation, this non-classicality decreases with the intervention of external magnetic field.
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We investigate the quantum correlations of a two-qubit XYZ Heisenberg spin-1/2 chain model with Dzyaloshinskii–Moriya interaction. The two-qubit system is considered in thermal equilibrium. The variations of logarithmic negativity, uncertainty-induced quantum nonlocality (UIN) and trace distance discord, versus the parameters characterizing the system, are analyzed. The results show that the UIN measure captures quantum correlations that cannot be revealed by entanglement and trace discord. We also show that the Dzyaloshinskii–Moriya interaction enhances the non-classical correlations between the spins and can weaken the undesirable destructive effects of thermal fluctuations. In addition, an entangled–unentangled phase transition can be detected from the behavior of logarithmic negativity.
We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional XYZ\mathit{XYZ}XYZ Heisenberg chain in thermal equilibrium depend on the temperature TTT of the bath and also on an external magnetic field BBB. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with TTT when entanglement decreases, cases where QD increases with TTT even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite TTT. We also show that by properly tuning BBB or the interaction between the qubits we get nonzero QD for any TTT and we present an effect not seen for entanglement, the ``regrowth'' of thermal QD.
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 behaviors of thermal entanglement, quantum correlation beyond entanglement namely, measurement-induced nonlocality (MIN) and coherence in a nickel radical molecular magnet (Et3NH)[Ni(hfac)2L], whose spin-spin interactions are well described by the Heisenberg model. Using experimentally estimated coupling parameters, we compute the thermal state of the system and analyze the dependence of quantum resources on temperature and magnetic field. The results indicate that the quantum resources of the nickel-radical molecular magnet persist even at room temperature. We show that while negativity (the entanglement measure) rapidly vanishes with increasing temperature and magnetic field, measurement-induced nonlocality and quantum coherence remain comparatively more stable and persist in regions where entanglement is absent. These results highlight the significance of nonclassical correlations beyond entanglement in thermally activated spin systems and suggest that such molecular magnets could serve as viable platforms for quantum information processing in realistic conditions.