Stationary ensemble approximations of dynamic quantum states: Optimizing the generalized Gibbs ensemble

Sels, Dries; Wouters, Michiel

doi:10.1103/physreve.92.022123

Cited by 12 publications

(13 citation statements)

References 42 publications

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“…It is often clear what suitable sets of constants of motion are, for example in quenches to integrable systems. In situations in which these constants of motion are ambiguous, the GGE inherits the same ambiguity [264][265][266][267]. As pointed out in the previous subsection, if all constants of motion are taken into account, then all finite dimensional systems equilibrate on average to the respective GGE if they equilibrate on average at all [254].…”

Section: Generalised Gibbs Ensemblesmentioning

confidence: 99%

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

2016

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We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

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Section: Generalised Gibbs Ensemblesmentioning

confidence: 99%

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

2016

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“…Within this approach, the notion of physically relevant is provided by how much an observable is able to reduce the distance between the GGE and the diagonal ensemble by being added into the set of conserved quantities that defines the GGE. More specifically, in [69] the distance between the time averaged state and the GGE is taken by the Kullback-Leibler (KL) distance (relative entropy) leading to which is always positive and where we have omitted the initial state ρ for brevity. In practice, given an 0 e > , the conserved quantities are successively added to the set of conserved…”

Section: Appendix a Conserved Quantities On The Ggementioning

confidence: 99%

Work and entropy production in generalised Gibbs ensembles

Perarnau-Llobet

Riera

Gallego³

et al. 2016

New J. Phys.

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Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble, reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.

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“…where Z rGGE ≡ tr{exp[· · · ]} (see Refs. [48,86,87] for similar concepts). Note that {κ lm··· } are determined from the condition ψ 0 |Q lQm · · · |ψ 0 = Tr[ρ rGGEQlQm · · · ].…”

Section: Verification Of the Eth For Each Symmetry Sectormentioning

confidence: 99%

Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries

2016

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We numerically study the unitary time evolution of a nonintegrable model of hard-core bosons with an extensive number of local Z2 symmetries. We find that the expectation values of local observables in the stationary state are described better by the generalized Gibbs ensemble (GGE) than by the canonical ensemble. We also find that the eigenstate thermalization hypothesis fails for the entire spectrum, but holds true within each symmetry sector, which justifies the GGE. In contrast, if the model has only one global Z2 symmetry or a size-independent number of local Z2 symmetries, we find that the stationary state is described by the canonical ensemble. Thus, the GGE is necessary to describe the stationary state even in a nonintegrable system if it has an extensive number of local symmetries.

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Stationary ensemble approximations of dynamic quantum states: Optimizing the generalized Gibbs ensemble

Cited by 12 publications

References 42 publications

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

Work and entropy production in generalised Gibbs ensembles

Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries

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