Abstract
These are lecture notes for a short course given at the Les Houches Summer School on ``Integrability in Atomic and Condensed Matter Physics'', in summer 2018. Here, I pedagogically discuss recent advances in the study of the entanglement spreading during the non-equilibrium dynamics of isolated integrable quantum systems. I first introduce the idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics and then join such an idea with the quasiparticle picture for the entanglement spreading to provide quantitive predictions for the time evolution of the entanglement entropy in arbitrary integrable models, regardless of the interaction strength.
Highlights
These are lecture notes for a short course given at the Les Houches Summer School on “Integrability in Atomic and Condensed Matter Physics”, in summer 2018
Pedagogically discuss recent advances in the study of the entanglement spreading during the non-equilibrium dynamics of isolated integrable quantum systems
I first introduce the idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics and join such an idea with the quasiparticle picture for the entanglement spreading to provide quantitive predictions for the time evolution of the entanglement entropy in arbitrary integrable models, regardless of the interaction strength
Summary
Cold atoms and ions which can probe closed quantum systems for time scales large enough to access the relaxation and thermalisation, see, e.g., the experiments in Refs. [4,5,6,7,8,9,10,11,12,13]. In some cases (to be better discussed in the following), these stationary values coincide with those in a thermal ensemble or suitable generalisations, despite the fact that the dynamics governing the evolution is unitary and the initial state is pure. Such relaxation is, at first, surprising because it creates a tension between the reversibility of the unitary dynamics and irreversibility of statistical mechanics. I will not make any introduction to integrability techniques in and out of equilibrium because they are the subject of other lectures in the 2018 Les Housches school [20,21,22,23] These lecture notes are organised as follows.
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