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arXiv:1505.03748 · Quantum Information Processing

Contributions of different parts of spin–spin interactions to quantum correlations in a spin ring model in an external magnetic field

Serge I. Doronin, Edward B. Fel’dman, E. I. Kuznetsova

Published May 22, 2015• 4 citations
arXivHTMLPDF
DOI
10.1007/s11128-015-1031-z

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We consider a spin ring with an arbitrary number of spins on the ring and one spin in its center in a strong external magnetic field.The spins on the ring are connected by the secular dipole-dipole interactions and interact with the central spin through the Heisenberg zz-interaction.We show that the quantum discord, describing quantum correlations between the ring and the central spin, can be obtained analytically for an arbitrary number of the spins in the high-temperature approximation.We demonstrate the evolution of quantum correlations at different numbers of the spins.The contributions of longitudinal and transversal spin interactions to the quantum discord are discussed.
The method for calculating the isotropic exchange interactions in the paramagnetic phase is proposed. It is based on the mapping of the high-temperature expansion of the spin-spin correlation function calculated for the Heisenberg model onto the Hubbard Hamiltonian one. The resulting expression for the exchange interaction has a compact and transparent formulation. The quality of the calculated exchange interactions is estimated by comparing the eigenvalue spectra of the Heisenberg model and low-energy magnetic part of the Hubbard model. By the example of quantum rings at half-filling with different hopping setups, we analyze contributions from different parts of the Hubbard model spectrum to the resulting exchange interaction. The developed method can be applied for simulating magnetic couplings in correlated materials and surface nanostructures.
In this paper, we study the thermal dynamics of quantum correlations and uncertainty relation in a three-qubit spin chain under the effect of Hamiltonian XY model, Dzyaloshinskii–Moriya (DM) interaction and external magnetic field. The results show that quantum correlations behave contrary to uncertainty under the effect of thermal dynamics and external magnetic field. However, they evolve in the same way under effect of DM interaction and spin coupling. DM interaction, magnetic field and spin coupling enhance quantum correlations.