Lindblad dynamics of the quantum spherical model

Sascha Wald, Gabriel T. Landi, Malte Henkel

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12 Citations (Scopus)
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The purely relaxational non-equilibrium dynamics of the quantum spherical model as described through a Lindblad equation is analysed. It is shown that the phenomenological requirements of reproducing the exact quantum equilibrium state as stationary solution and the associated classical Langevin equation in the classical limit $g\to 0$ fix the form of the Lindblad dissipators, up to an overall time-scale. In the semi-classical limit, the models' behaviour become effectively the one of the classical analogue, with a dynamical exponent $z=2$, and an effective temperature $T_{\rm eff}$, renormalised by the quantum coupling $g$. A distinctive behaviour is found for a quantum quench, at zero temperature, deep into the ordered phase $g\ll g_c(d)$, for $d>1$ dimensions. Only for $d=2$ dimensions, a simple scaling behaviour holds true, with a dynamical exponent $z=1$, while for dimensions $d\ne 2$, logarithmic corrections to scaling arise. The spin-spin correlator, the growing length scale and the time-dependent susceptibility show the existence of several logarithmically different length scales.
Original languageEnglish
Article number013103
Number of pages61
JournalJournal of Statistical Mechanics: Theory and Experiment
Publication statusPublished - 22 Jan 2018
Externally publishedYes

Bibliographical note

This is the Accepted Manuscript version of an article accepted for publication in Journal of Statistical Mechanics: Theory and Experiment . IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1742-5468/aa9f44.

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.


  • quant-ph
  • cond-mat.stat-mech
  • hep-th
  • math-ph
  • math.MP
  • nlin.SI


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