Convergence radius of perturbative Lindblad-driven nonequilibrium steady states

Physical Review. E
Humberto C F Lemos, Tomaž Prosen

Abstract

We address the problem of analyzing the radius of convergence of perturbative expansion of nonequilibrium steady states of Lindblad-driven spin chains. A simple formal approach is developed for systematically computing the perturbative expansion of small driven systems. We consider the paradigmatic model of an open XXZ spin-1/2 chain with boundary-supported ultralocal Lindblad dissipators and treat two different perturbative cases: (i) expansion in the system-bath coupling parameter and (ii) expansion in the driving (bias) parameter. In the first case (i) we find that the radius of convergence quickly shrinks with increasing the system size, while in the second case (ii) we find that the convergence radius is always larger than 1, and in particular it approaches 1 from above as we change the anisotropy from an easy-plane (XY) to an easy-axis (Ising) regime.

References

Feb 6, 1995·Physical Review Letters·H CastellaP Prelovsek
Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hannu WichterichMathias Michel
Oct 27, 2011·Physical Review Letters·Tomaž Prosen
Jan 25, 2013·Physical Review Letters·D KarevskiG M Schütz

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Citations

May 20, 2020·Physical Review. E·Tatsuhiko Shirai, Takashi Mori

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