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Modern Physics Letters B

THERMAL AND NON-UNIFORM MAGNETIC QUANTUM DISCORD IN THE TWO-QUBIT HEISENBERG XXZ MODEL

Rui-Hua Xiao, Zhan-Ying Guo, Fang Jian-Xing

Published Feb 2, 2012• 3 citations
Publisher

Abstract

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 ).

DOI
10.1142/s021798491150028x

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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 ).
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.
The thermal quantum discord (QD) is studied in a two-qubit Heisenberg XXZ system with Dzyaloshinskü–Moriya (DM) interaction. We compare the thermal QD with thermal entanglement in this system and find remarkable differences between them. For instance, we show situations where QD decreases asymptotically to zero with temperature T while entanglement decreases to zero at the point of critical temperature, situations where QD decreases with certain tunable parameters such as D z and D x when entanglement increases. We find that the characteristic of QD is exotic in this system and this possibly offers a potential solution to enhance entanglement of a system. We also show that tunable parameter D x is more efficient than parameter D z in most regions for controlling the QD.
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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.
Two kinds of thermal quantum correlations, measured respectively by quantum discord (QD) and the generalized negativity (GN), are studied for various magnetic fields, couplings, and temperatures in a two-qubit Heisenberg XYZ model. It is shown that QD and GN can exhibit a similar behavior in some regions of magnetic field, coupling, and temperature, while they behave in a contrary manner in other regions. For example, QD may increase with suitable magnetic fields, couplings, and temperature when GN decreases. QD is more robust against temperature than GN, and can reveal a kink at a suitable coupling at finite temperature while GN cannot. Moreover, a nearly unchanged QD or GN can be obtained in a large region of magnetic field, coupling, and temperature. These adjustable QD and GN via the varied magnetic field, coupling, and temperature may have significant applications in quantum information processing.