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arXiv:1205.3126 · Physica Scripta

Comments on a boundary-driven openXXZchain: asymmetric driving and uniqueness of steady states

Tomaž Prosen

Published Oct 19, 2012• 46 citations
arXivHTMLPDF

Abstract

In this paper, we provide two extensions of recent explicit results on the matrix-product ansatz for the non-equilibrium steady state of a Markovian boundary-driven anisotropic Heisenberg XXZ spin-1/2 chain. We write a perturbative solution for the steady-state density matrix in the system–bath coupling for an arbitrary (asymmetric) set of four spin-flip rates at the two chain ends, generalizing the symmetric-driving ansatz of Prosen (2011 Phys. Rev. Lett. 106 217206). Furthermore, we generalize the exact (non-perturbative) form of the steady state for just two Lindblad channels (spin-up flipping on the left and spin-down flipping on the right) to an arbitrary (asymmetric) ratio of the spin-flipping rates (Prosen 2011 Phys. Rev. Lett. 107 137201). In addition, we also indicate a simple proof of the uniqueness of our steady states.

DOI
10.1088/0031-8949/86/05/058511

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