Dynamical many-body localization in an integrable model

Keser, Aydın Cem; Ganeshan, Sriram; Refael, Gil; Galitski, Victor

doi:10.1103/physrevb.94.085120

Cited by 29 publications

(24 citation statements)

References 33 publications

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“…If generalized to a many-body system of QRKRs, this statement results in DMBL similar to that found in Ref. [47], but for a nonintegrable system. Independently of the numerics, but in agreement with it, we argue that this is the case because the difference between the dynamics of the many-body QRKRs model and the integrable model considered in Ref.…”

Section: Introductionsupporting

confidence: 80%

“…Independently of the numerics, but in agreement with it, we argue that this is the case because the difference between the dynamics of the many-body QRKRs model and the integrable model considered in Ref. [47] vanishes as the angular-momentum terms increase and overwhelm the mass terms.…”

Section: Introductionsupporting

confidence: 58%

“…Although dynamical localization for two coupled QKRs was predicted to disappear in the presence of coordinate-dependent interactions 12,19 , in 2007 Toloui et al 46 reported localized regimes in two coupled QKRs. Furthermore, recently Keser et al 47 showed that coupled many-body systems can possess dynamical localization, and the corresponding phenomenon was dubbed dynamical many-body localization (DMBL). However, DMBL has been found only for a specific integrable system of linear quantum kicked rotors (LQKRs) so far, and the existence of this phenomenon in more general, nonintegrable cases remains unclear.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical localization of coupled relativistic kicked rotors

Rozenbaum

Galitski

2017

Phys. Rev. B

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A periodically-driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work, Phys. Rev. B 94, 085120 (2016), Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study non-integrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that DMBL can exist in generic, non-integrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since many-body linear model is a high-angularmomentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.

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Section: Introductionsupporting

confidence: 80%

Section: Introductionsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

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Dynamical localization of coupled relativistic kicked rotors

Rozenbaum

Galitski

2017

Phys. Rev. B

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“…Further, we note that there has been recent interest in dynamical localization in periodically driven many-body systems [17,[19][20][21][22][23][24]. In such studies, numerical simulations are a useful tool.…”

Section: Discussionmentioning

confidence: 99%

Exponentially Slow Heating in Periodically Driven Many-Body Systems

Roeck²,

2015

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We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that for systems with local interactions, energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including decay of highly energetic excitations in cold atomic and solid-state systems.

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“…In ref. 10 a similar problem was studied for a simpler, integrable model of linear rotors9, where localization can survive in the presence of interactions due to integrability. The authors of ref.…”

mentioning

confidence: 99%

Interacting ultracold atomic kicked rotors: loss of dynamical localization

Qin

Andreanov

Park

et al. 2017

Sci Rep

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We study the fate of dynamical localization of two quantum kicked rotors with contact interaction, which relates to experimental realizations of the rotors with ultra-cold atomic gases. A single kicked rotor is known to exhibit dynamical localization, which takes place in momentum space. The contact interaction affects the evolution of the relative momentum k of a pair of interacting rotors in a non-analytic way. Consequently the evolution operator U is exciting large relative momenta with amplitudes which decay only as a power law 1/k4. This is in contrast to the center-of-mass momentum K for which the amplitudes excited by U decay superexponentially fast with K. Therefore dynamical localization is preserved for the center-of-mass momentum, but destroyed for the relative momentum for any nonzero strength of interaction.

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Dynamical many-body localization in an integrable model

Cited by 29 publications

References 33 publications

Dynamical localization of coupled relativistic kicked rotors

Dynamical localization of coupled relativistic kicked rotors

Exponentially Slow Heating in Periodically Driven Many-Body Systems

Interacting ultracold atomic kicked rotors: loss of dynamical localization

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