Behavior of magnetic currents in anisotropic Heisenberg spin chains out of equilibrium

Popkov, V.; Schütz, G.M.; Salerno, M.

doi:10.1103/PhysRevE.85.031137

Journal Article

PreJuSER-20484

Behavior of magnetic currents in anisotropic Heisenberg spin chains out of equilibrium

Popkov, V.FZJ* ; Salerno, M.FZJ* ; Schütz, G. M.FZJ*

2012
APS College Park, Md.

Physical review / E 85(3), 031137 (2012) [10.1103/PhysRevE.85.031137]

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Please use a persistent id in citations: http://hdl.handle.net/2128/9267 doi:10.1103/PhysRevE.85.031137

Abstract: The behavior of the magnetic currents in one-dimensional Heisenberg XXZ spin chains kept out of equilibrium by boundary driving fields is investigated. In particular, the dependence of the spin currents on the anisotropy parameter Delta and on the boundary fields is studied both analytically and numerically in the framework of the Lindblad master equation formalism. We show that the spin current can be maximized with appropriate choices of the boundary fields, and for odd system sizes, N, we demonstrate the existence of additional symmetries that cause the current to be an odd function of Delta. From direct numerical integrations of the quantum master equation, we find that for an arbitrary N the current J(z)(N) vanishes for Delta = 0, while for Delta negative it alternates its sign with the system size. In the gapless critical region |Delta| < 1, the scaling of the current is shown to be J(z)(N) similar to 1/N while in the gapped region |Delta| > 1 we find that J(z) (N) similar to exp(-alpha N). A simple mean-field approach, which predicts rather well the values of J(z) (N) for the gapped region and the values of the absolute current maxima in the critical region, is developed. The existence of two different stationary solutions for the mean-field density matrix in the whole parameter range is also demonstrated.

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Note: V.P. acknowledges the University of Salerno for a research grant to support this work. M. S. acknowledges support from the Ministero dell' Istruzione, dell' Universita e della Ricerca (MIUR) through a Programma di Ricerca Scientifica di Rilevante Interesse Nazionale (PRIN) initiative.

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