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arXiv:1105.4208 · Physics Letters A

Generation of non-equilibrium thermal quantum discord and entanglement in a three-spin XX chain by multi-spin interaction and an external magnetic field

Xiu-Xing Zhang, Fuli Li

Published Oct 12, 2011• 7 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2011.10.004

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We have investigated the quantum discord (QD) of the thermal density matrix of spin-1/2 Heisenberg chains with Dzyaloshinskii–Moriya (DM) interaction. With fermionization technique, we study the mutual effect of DM interaction and the external magnetic field on the QD and the entanglement. Our analysis implies that the DM interaction can enhance the QD while the external magnetic field will shrink the QD. By a comparison between the entanglement and the QD, we find that the QD is more robust to the temperature and to the external magnetic field than the entanglement of formation (EoF) in the sense that the EoF takes a zero value while the QD does not for high temperature and strong external magnetic field. This point confirms the conclusion that there exist some separable states containing non-zero QD.
We investigate how thermal quantum discord (QD) and classical correlations (CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on the temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behavior of QD differs in many unexpected ways from the thermal entanglement (EOF). For the nonuniform case ( B 1 = − B 2 ), we find that QD and CC are equal for all values of ( B 1 = − B 2 ) and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which QD and CC are equal. The specification of this class and the corresponding conditions are completely general and apply to any quantum system in a state in this class satisfying these conditions. We further find that the relative contributions of QD and CC can be controlled easily by changing the relative magnitudes of B 1 and B 2 . Finally, we connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environment.