The overlap distribution for a non-random frustrated Ising model

Nachtergaele, Bruno; Slegers, L.

doi:10.1088/0305-4470/21/2/030

Cited by 6 publications

(6 citation statements)

References 12 publications

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“…Let us finally discuss the connection between our results and Lieb-Robinson bounds. 5 Initially, the Lieb-Robinson bounds were formulated for the non-equal time commutator of two spins in a lattice model: this commutator is exponentially small outside the light cone. 3 One can use this to show that even in a non-relativistic theory the speed of the propagation of information is limited by the Lieb-Robinson bound.…”

Section: Discussionmentioning

confidence: 99%

“…Due to the importance of understanding the spread of entanglement in quantum information processing and efficient numerical simulation methods, a lot of theoretical work has since then been done to gener-alize the original work by Lieb and Robinson to other situations and more general questions. [4][5][6][7] Numerically, the light cone effect has been seen in a number of lattice models. 8,9 Recently, it was also observed experimentally after a quench in a cold atomic gas with very good agreement with theoretical results.…”

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal buildup of the Kondo screening cloud

2013

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We investigate how the Kondo screening cloud builds up as a function of space and time. Starting from an impurity spin decoupled from the conduction band, the Kondo coupling is switched on at time t=0. We work at the Toulouse point where one can obtain exact analytical results for the ensuing spin dynamics at both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts building up in the wake of the impurity spin being transported to infinity. In this buildup process the impurity spin--conduction band spin susceptibility shows a sharp light cone due to causality, while the corresponding correlation function has a tail outside the light cone. At T=0 this tail has a power law decay as a function of distance from the impurity, which we interpret as due to initial entanglement in the Fermi sea.Comment: 10 pages, 9 figure

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatiotemporal buildup of the Kondo screening cloud

2013

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“…An important tool for the study of equilibration phenomena is provided by Lieb-Robinson bounds [72,154,155]. They limit the speed at which excitations can travel through a quantum lattice system equipped with a locally interacting Hamiltonian.…”

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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“…Over the past few years applications have driven a number of interesting generalizations of the original Lieb-Robinson bounds. Several review articles have been devoted to many of these specific applications, see [8,29], and some lecture notes from schools on topics concerning locality are now available [30,31]. In this short note, we make no attempt to give an exhaustive list of generalizations and applications, but rather we list many relevant works to give the interested reader a reasonable starting point to further investigate this active area of research.…”

Section: Some Words On Generalizations and Applicationsmentioning

confidence: 99%