Density correlations and transport in models of many‐body localization

Prelovšek, P.; Mierzejewski, Marcin; Barišić, O. S.; Herbrych, Jacek

doi:10.1002/andp.201600362

Cited by 45 publications

(56 citation statements)

References 79 publications

(188 reference statements)

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“…So, we understand that the numerical value α=1 is subject to a significant uncertainty. The same group later extended their studies to related correlation functions 30,62 . Reminiscent of creep, also in these correlators a very slow dynamics with significant finite-size effects can be identified, e.g., in Fig.…”

Section: Relation To Earlier Studiesmentioning

confidence: 99%

“…is being analyzed. Even though the diffusion propagator Φ(x, t) has been studied before, 29,30,36,37 it is not the usual object of investigation. When the exponent β has been considered, it has mostly been derived from closely related observables, such as the frequency dependent conductivity at zero wavenumber calculated in finite size systems [38][39][40][41][42] .…”

Section: Introductionmentioning

confidence: 99%

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Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

2019

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We investigate charge relaxation in disordered and quasi-periodic quantum-wires of spin-less fermions (t−V -model) at different inhomogeneity strength W in the localized and nearly-localized regime. Our observable is the time-dependent density correlation function, Φ(x, t), at infinite temperature. We find that disordered and quasi-periodic models behave qualitatively similar: Although even at longest observation times the width ∆x(t) of Φ(x, t) does not exceed significantly the noninteracting localization length, ξ0, strong finite-size effects are encountered. Our findings appear difficult to reconcile with the rare-region physics (Griffiths effects) that often is invoked as an explanation for the slow dynamics observed by us and earlier computational studies. Motivated by our numerical data we discuss a scenario in which the MBL-phase splits into two subphases: in MBLA ∆x(t) diverges slower than any power, while it converges towards a finite value in MBLB . Within the scenario the transition between MBLA and the ergodic phase is characterized by a length scale, ξ, that exhibits an essential singularity ln ξ ∼ 1/|W − Wc 1 |. Relations to earlier numerics and proposals of two-phase scenarios will be discussed. arXiv:1904.06928v2 [cond-mat.str-el]

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Section: Relation To Earlier Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

2019

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“…In particular, it is believed that g → ∞ in the thermodynamic limit, both for the ergodic and the sub-diffusive phase. Instead, in the MBL phase g → constant < ∞ [12]. In the light of Eq.…”

Section: Consider a Complete Orthonormal Family Of Statesmentioning

confidence: 95%

Quantum coherence and the localization transition

et al. 2019

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A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation precise, we study the localization transition via quantum coherence measures arising from the resource theory of coherence. We show that the escape probability, which is known to show distinct behavior in the ergodic and localized phases, arises naturally as the average of a coherence measure. Moreover, using the theory of majorization, we argue that broad families of coherence measures can detect the uniformity of the transition matrix (between the Hamiltonian and configuration bases) and hence act as probes to localization. We provide supporting numerical evidence for Anderson and Many-Body Localization (MBL).For infinitesimal perturbations of the Hamiltonian, the differential coherence defines an associated Riemannian metric. We show that the latter is exactly given by the dynamical conductivity, a quantity of experimental relevance which is known to have a distinctively different behavior in the ergodic and in the many-body localized phases. Our results suggest that the quantum informationtheoretic notion of coherence and its associated geometrical structures can provide useful insights into the elusive nature of the ergodic-MBL transition.arXiv:1906.09242v2 [quant-ph]

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“…44,47 Moreover, the connection of HCB to spin systems in 1D allows closer relation with the disordered Hubbard model 53,54,67 and the disordered Heisenberg model. 4,56,63 Using the standard relation of HCB with S = 1/2 local spin operators, we can follow previous procedure and eliminate the diagonal l = l term via local transformation U l = i U li ,…”

Section: Hard-core Bosonsmentioning

confidence: 99%

“…54 Such a Griffiths-type mechanism for subdiffusion has been invoked also for the ergodic side of the 1D Heisenberg model with random magnetic fields, [55][56][57][58][59][60] although some results indicate that this might be a transient feature to normal diffusion. [61][62][63] In this paper we consider the propagation of a SP in a random chain, coupled to dispersive bosons, which can be either NB or HCB, whereby the latter case simulates coupling to spins. We analyze the dynamics in terms of the rate equations for the particle hopping between the Anderson eigenstates.…”

Section: Introductionmentioning

confidence: 99%

Transient and persistent particle subdiffusion in a disordered chain coupled to bosons

2018

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We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between dynamics due to noninteracting bosons and hard-core bosons. In the first case the transient dynamics is subdiffusive, but multi-boson processes allow for long-time normal diffusion, while hard-core effects suppress multi-boson processes leading to persistent subdiffusive transport, consistent with numerical results for a full many-body evolution. In contrast, analogous study for a quasiperiodic potential reveals a stable long-time diffusion.

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Density correlations and transport in models of many‐body localization

Cited by 45 publications

References 79 publications

Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

Quantum coherence and the localization transition

Transient and persistent particle subdiffusion in a disordered chain coupled to bosons

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