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On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions

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Abstract

The anisotropic Heisenberg two-spin-1/2 model in an inhomogeneous magnetic field with both antisymmetric Dzyaloshinsky–Moriya and symmetric Kaplan–Shekhtman–Entin-Wohlman–Aharony cross interactions is considered at thermal equilibrium. Using a group-theoretical approach, we find fifteen spin Hamiltonians and as many corresponding Gibbs density matrices (quantum states) whose eigenvalues are expressed only through square radicals. We also found local unitary transformations that connect nine of this fifteen state collection, and one of them is the X quantum state. Since such quantum correlations as quantum entanglement, quantum discord, one-way quantum work deficit, and others are known for the X state, this allows to get the quantum correlations for any member from the nine state family. Further, we show that the remaining six quantum states are separable and that they are also connected by local unitary transformations, but, however, now the case with known correlations beyond entanglement is generally not available.

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Notes

  1. One may also choose \({\tilde{Y}}=\frac{1}{\sqrt{2}} \left( \begin{array}{ll} 1&{}i\\ i&{}1 \end{array} \right) \) that leads to the relations \({\tilde{Y}}^\dagger \sigma _x {\tilde{Y}}=\sigma _x\), \({\tilde{Y}}^\dagger \sigma _y {\tilde{Y}}=\sigma _z\), and \({\tilde{Y}}^\dagger \sigma _z {\tilde{Y}}=-\sigma _y\).

  2. We omit the case \(U_{00} (=E)\) because \(\{E\}\) is the trivial group.

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Acknowledgements

This work was performed as a part of the state task of the RF, CITIS # AAAA-A19-119071190017-7.

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  1. Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 142432, Moscow Region, Russia

    M. A. Yurischev

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Yurischev, M.A. On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions. Quantum Inf Process 19, 336 (2020). https://doi.org/10.1007/s11128-020-02835-x

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