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arXiv · 1801.07646

Time-dependent generalized Gibbs ensembles in open quantum systems

Florian Lange·Zala Lenarčič·Achim Rosch
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Abstract

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which both break integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time-evolution on long time-scales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

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Florian Lange, Zala Lenarčič, Achim Rosch. 2018-01-23. Time-dependent generalized Gibbs ensembles in open quantum systems. https://doi.org/10.1103/physrevb.97.165138

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