Many-body dynamical localization in the kicked Bose-Hubbard chain

Fava, Michele; Fazio, Rosario; Russomanno, Angelo

doi:10.1103/physrevb.101.064302

Cited by 20 publications

(12 citation statements)

References 65 publications

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“…When J = 0, the Hamiltonian (1) behaves as the operatorV , therefore it shows massively degenerate eigenspaces, as elucidated in Ref. [17]. If we switch on a small value of J U , we find a strong mixing inside the eigenspaces, while different eigenspaces interact starting from second perturbative order in J/U .…”

Section: Appendix A: Derivation Of the Effective Xxz Model Via Perturmentioning

confidence: 52%

“…A striking example is dynamical localization (initially discovered for one degree of freedom [14] and later generalized to the many body case [15][16][17][18]), where a classical ergodic driven system shows a regular-like behavior in the quantum regime, leading to a suppression of energy absorption. Another example is many body localization.…”

Section: Introductionmentioning

confidence: 99%

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Nonergodic behavior of the clean Bose-Hubbard chain

2020

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We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a nonergodic regime by means of indicators as the half-chain entanglement entropy of the eigenstates, the average level spacing ratio, the properties of the eigenstate-expectation distribution of the correlation and the scaling of the inverse participation ratio averages. We find that this ergodicity breaking is different from many-body localization because the average half-chain entanglement entropy of the eigenstates obeys volume law. This ergodicity breaking appears unrelated to the spectrum being organized in quasidegenerate multiplets at small hopping and finite system sizes, so in principle, it can survive also for larger system sizes. We find that some imbalance oscillations in time which could mark the existence of glassy behavior in space are well described by the dynamics of a single symmetry-breaking doublet and quantitatively captured by a perturbative effective XXZ model. We show that the amplitude of these oscillations vanishes in the large-size limit. Our findings are numerically obtained for systems for L < 12. Extrapolations of our scalings to larger system sizes should be taken with care, as discussed in the paper.

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Section: Appendix A: Derivation Of the Effective Xxz Model Via Perturmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Nonergodic behavior of the clean Bose-Hubbard chain

2020

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“…In the case of a single kicked rotor, quantum coherence strongly suppresses heating through dynamical localization in energy space [32,33]. Accordingly, it was recently shown that dynamical localization can lead to ergodicity breaking in many-body kicked models, such as coupled rotors [34] and the Bose-Hubbard model [35]. However, as conjectured in Ref.…”

Section: Discussionmentioning

confidence: 92%

Statistical Floquet prethermalization of the Bose-Hubbard model

Torre

Dentelski

2021

SciPost Phys.

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The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, such exponential suppression of heating has been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

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“…This phenomenon has a dynamical counterpart originally studied in the context of the kicked rotor [3][4][5][6]. Localization is an extremely broad subject that extends to the hydrogen atom in a monochromatic field [7,8], Rydberg atoms [9], quantum billiards [10][11][12][13][14][15][16], banded random matrices [17], interacting systems [18][19][20][21][22], and kicked interacting systems [23][24][25][26], among others.…”

Section: Introductionmentioning

confidence: 99%

Identification of quantum scars via phase-space localization measures

Pilatowsky-Cameo,

Villaseñor,

Bastarrachea-Magnani

et al. 2021

Preprint

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There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the α-moments of the Husimi function and is known as the Rényi occupation of order α. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spinboson model with an unbounded four-dimensional phase space, we show that the Rényi occupations with large α are highly effective at revealing quantum scars. Furthermore, by analyzing the large moments of the Husimi function, we are able to find the unstable periodic orbits that scar some of the eigenstates of the model.

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Many-body dynamical localization in the kicked Bose-Hubbard chain

Cited by 20 publications

References 65 publications

Nonergodic behavior of the clean Bose-Hubbard chain

Nonergodic behavior of the clean Bose-Hubbard chain

Statistical Floquet prethermalization of the Bose-Hubbard model

Identification of quantum scars via phase-space localization measures

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