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Nachtergaele, Lode; Gijbels, Toon; Bormans, J.; Catthoor, Francky; Bolsens, I.

doi:10.1023/a:1008135917341

Cited by 5 publications

(3 citation statements)

References 27 publications

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“…Such "light-cone"-like dynamics has been systematically explored and put into the context of equilibration analytically and numerically [77-79, 111, 112, 156-160] as well as experimentally [21,27,28,30,161]. Similar bounds also exist for more general settings, like local Liouvillian dynamics [75,162,163], exponentially decaying but no longer strictly local interactions [72], as well as for certain long-ranged, i.e., power law like decaying, interactions [72,159,164] as long as the exponent is sufficiently large. Such long-ranged interactions have been experimentally investigated in systems of trapped ions [21,161].…”

Section: Lieb-robinson Boundsmentioning

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: Lieb-robinson Boundsmentioning

confidence: 99%

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

2016

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“…Long-range generalization of Lieb-Robinson bounds.-Using standard techniques [1,2,8,35,37], Q r (t) can be bounded by an infinite series in time,…”

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confidence: 99%

Persistence of Locality in Systems with Power-Law Interactions

et al. 2014

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Motivated by recent experiments with ultracold matter, we derive a new bound on the propagation of information in D-dimensional lattice models exhibiting 1/r^{α} interactions with α>D. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, whereas the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, qualitatively reproduce the short- and long-distance dynamical behavior following a local quench in an XY chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems.

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“…where the operator norm is defined by O = sup |ψ O|ψ / |ψ . Following the Lieb-Robinson bound in closed systems [47][48][49], an inequality has been proved in open quantum systems [50][51][52][53][54]…”

Section: The Width Of the Partially Recovered Light Conementioning

confidence: 99%

Information scrambling in chaotic systems with dissipation

2019

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Chaotic dynamics in closed local quantum systems scrambles quantum information, which is manifested quantitatively in the decay of the out-of-time-ordered correlators (OTOC) of local operators. How is information scrambling affected when the system is coupled to the environment and suffers from dissipation? In this paper, we address this question by defining a dissipative version of OTOC and numerically study its behavior in a prototypical chaotic quantum chain in the presence of dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the 'information light cone' can only reach a finite distance even when the effect of overall decay is removed. Based on this observation we conjecture a modified version of the Lieb-Robinson bound in dissipative systems.

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Cited by 5 publications

References 27 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

Persistence of Locality in Systems with Power-Law Interactions

Information scrambling in chaotic systems with dissipation

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