Multifractality and its role in anomalous transport in the disordered  XXZ spin-chain

Luitz, David J.; Khaymovich, Ivan M.; Lev, Yevgeny Bar

doi:10.21468/scipostphyscore.2.2.006

Cited by 79 publications

(69 citation statements)

References 83 publications

(158 reference statements)

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“…Note further that Serbyn et al [67] do not include multifractality into their argument, effectively letting α = 1. In hindsight, this appears to be an oversimplification since in the MBL-regime multifractality tends to be strong [77][78][79][80][81][82].…”

Section: Heuristic Argument Linking Dephasing and Multifractalitymentioning

confidence: 99%

Dephasing in strongly disordered interacting quantum wires

2021

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Many-body localization is a fascinating theoretical concept describing the intricate interplay of quantum interference, i.e., localization, with many-body interaction-induced dephasing. Numerous computational tests and also several experiments have been put forward to support the basic concept. Typically, averages of time-dependent global observables have been considered, such as the charge imbalance. We here investigate within the disordered spinless Hubbard (t-V ) model how dephasing manifests in time-dependent variances of observables. We find that after quenching a Néel state the local charge density exhibits strong temporal fluctuations with a damping that is sensitive to disorder W : variances decay in a power-law manner, t −ζ , with an exponent ζ (W ) strongly varying with W . A heuristic argument suggests the form ζ ≈ α(W )ξ sp , where ξ sp (W ) denotes the noninteracting localization length and α(W ) characterizes the multifractal structure of the dynamically active volume fraction of the many-body Hilbert space. In order to elucidate correlations underlying the damping mechanism, exact computations are compared with results from the time-dependent Hartree-Fock approximation. Implications for experimentally relevant observables, such as the imbalance, will be discussed.

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Section: Heuristic Argument Linking Dephasing and Multifractalitymentioning

confidence: 99%

Dephasing in strongly disordered interacting quantum wires

2021

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“…While the model (1) has been studied in great detail, the critical disorder is only known with a large margin of error, W c = 3.8 ± 1 [22,[31][32][33][34]. We therefore focus on quite strong disorder strengths to be sufficiently far from the critical regime, which is known to exhibit strong finite size effects [35][36][37].…”

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confidence: 99%

Absence of slow particle transport in the many-body localized phase

Luitz

Lev

2020

Phys. Rev. B

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We analyze the saturation value of the bipartite entanglement and number entropy starting from a random product state deep in the many-body localized (MBL) phase. By studying the probability distributions of these entropies we find that the growth of the saturation value of the entanglement entropy stems from a significant reshuffling of the weight in the probability distributions from the bulk to the exponential tails. In contrast, the probability distributions of the saturation value of the number entropy are converged with system size, and exhibit a sharp cutoff for values of the number entropy which correspond to one particle fluctuating across the boundary between the two halves of the system. Our results therefore rule out slow particle transport deep in the MBL phase and confirm that the slow entanglement entropy production stems uniquely from configurational entanglement.

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“…[23,54]. Dynamically, this region is dominated by sub-diffusive processes, multifractal scalings and other unexpected behavior [29][30][31][32]. The region in between the ergodic and the localized phases has been extensively studied.…”

Section: Model: the Disordered J 1 -J Chain And Many-body Localizationmentioning

confidence: 99%

Signatures of a critical point in the many-body localization transition

2021

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Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a possible finite-size precursor of a critical point that shows a typical finite-size scaling and distinguishes between two different dynamical phases. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered J_1J1-J_2J2 model. For system sizes accessible to exact diagonalization, both the position and the size of this maximum scale linearly with the system size. Furthermore, we show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide. Below this point, the spectral statistics follow the universal random matrix behavior up to the Thouless energy. Above it, no traces of chaotic behavior remain, and the spectral statistics are well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior. We provide, thus, an integrated scenario for the many-body localization transition, conjecturing that the critical point in the thermodynamic limit, if it exists, should be given by this value of disorder strength.

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Multifractality and its role in anomalous transport in the disordered XXZ spin-chain

Cited by 79 publications

References 83 publications

Dephasing in strongly disordered interacting quantum wires

Dephasing in strongly disordered interacting quantum wires

Absence of slow particle transport in the many-body localized phase

Signatures of a critical point in the many-body localization transition

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