Solution of the Lindblad equation for spin helix states

Physical Review. E
V Popkov, G M Schütz

Abstract

Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a nonvanishing spin current that is locally conserved except at the boundaries. We demonstrate that with suitably chosen boundary target states one can solve the many-body Lindblad equation exactly in any dimension. As solution we obtain pure states at any finite value of the dissipation strength and any system size. They are characterized by a helical stationary magnetization profile and a ballistic spin current which is independent of system size, even when the quantum spin system is not integrable. These results are derived in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its higher-spin generalizations, which include the integrable spin-1 Zamolodchikov-Fateev model and the biquadratic Heisenberg chain.

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Aug 21, 2013·Physical Review Letters·Tomaž Prosen, Enej Ilievski
Feb 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V PopkovG M Schütz
May 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marko Žnidarič
Jan 25, 2013·Physical Review Letters·D KarevskiG M Schütz
Nov 26, 2016·Physical Review Letters·Bruno BertiniMaurizio Fagotti

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Citations

Jan 20, 2018·Physical Review. E·Federico CarolloCarlos Pérez-Espigares
Mar 20, 2018·Physical Review. E·Emmanuel Pereira
Apr 2, 2019·Physical Review Letters·Thore Posske, Michael Thorwart
Jul 3, 2021·Physical Review Letters·Marius de LeeuwBalázs Pozsgay

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