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Thermal entanglement of a coupled electronic spins system: interplay between an external magnetic field, nuclear field and spin–orbit interaction

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Abstract

We have studied the thermal entanglement as a function of the temperature for a two-qubits Heisenberg spins system; we have included Dzyaloshinskii–Moriya interaction (DM), an external magnetic field (EMF) and hyperfine interaction due to the nuclear field of the surrounding nuclei. A critical value for the EMF was found, around \(B^{(c)}_{\mathrm{ext},z} \sim 39\) mT, which characterizes two regimes of behavior of the thermal entanglement. Our results show that the DM term acts as a facilitator for the entanglement because it prolongs the nonzero thermal entanglement for larger temperatures. We found that the concurrence as a function of the temperature has a local maximum, for values of the magnetic field larger than the critical field. We also show that the critical temperature \(T_\mathrm{c}\) follows a polynomial growth as a function of the DM term, with characteristic behavior \(T_{\mathrm{c}} \sim \beta _{0}^{2}\), and the hyperfine field implies a critical temperature as a function of the field variance, \(\sigma \) of the form \(T_{\mathrm{c}} \sim \sigma ^{2}\). We show that in this system, the entanglement measure by the concurrence and the one-spin polarization observable exhibit opposite behavior, providing a method to obtain the entanglement from the measurement of an observable.

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Acknowledgments

We would like to thanks DGAPA-UNAM for support with the Project IN112012 and R.G. thanks CONACYT and CICESE for financial aid with a PhD scholarship.

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Authors and Affiliations

  1. Centro de Ingeniería y Tecnología, Universidad Autónoma de Baja California, 21500, Tijuana, Baja California, Mexico

    Roberto J. Guerrero M.

  2. Departamento de Física Teórica, Centro Nanociencias y Nanotecnologia, Universidad Nacional Autónoma de México, Apartado Postal 361, 22800, Ensenada, Baja California, Mexico

    F. Rojas

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Correspondence to Roberto J. Guerrero M..

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Guerrero M., R.J., Rojas, F. Thermal entanglement of a coupled electronic spins system: interplay between an external magnetic field, nuclear field and spin–orbit interaction. Quantum Inf Process 14, 1973–1996 (2015). https://doi.org/10.1007/s11128-015-0946-8

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  • DOI: https://doi.org/10.1007/s11128-015-0946-8

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