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

Luitz, David J.; Lev, Yevgeny Bar

doi:10.1103/physrevb.102.100202

Cited by 76 publications

(38 citation statements)

References 44 publications

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“…[30,31] that the system is not localized up to at least D ∼ 40. While we already responded to the criticism of our results by Luitz and BarLev [53] in detail in [31] our current study has brought to light another issue: Performing averages over all initial product states leads to a 1/L correction to ∆N 2 with a negative sign which is present already in the non-interacting Anderson case and which can disguise the increase of ∆N 2 with system size in the interacting case. This might explain why this increase has been missed in the past including in [53].…”

Section: Discussionmentioning

confidence: 55%

Particle fluctuations and the failure of simple effective models for many-body localized phases

et al. 2022

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We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case (Anderson localization) and in effective models where only interaction terms diagonal in the Anderson basis are kept. We demonstrate that these types of simple effective models cannot account for the particle number fluctuations observed in the MBL phase of the microscopic model. This implies that assisted and pair hopping terms-generated when transforming the microscopic Hamiltonian into the Anderson basis-cannot be neglected even at strong disorder and weak interactions. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved local charges. If such a set of conserved local charges does not exist, then particles are expected to ultimately delocalize for any finite disorder strength.

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Section: Discussionmentioning

confidence: 55%

Particle fluctuations and the failure of simple effective models for many-body localized phases

et al. 2022

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“…Next, our probe could be relevant in the recently emerging debate on (2) (0, 0|1000) as a function of for L = 8 (squares), L = 10 (circles), and L = 12 (pentagons). For Poissonian and Wigner-Dyson level statistics, one expects, respectively, ρ (2) (0, 0|1000) = 1 and ρ (2) (0, 0|1000) ≈ 0.001. the stability of many-body localization [19,[44][45][46], in which the spectral form factor plays a prominent role. We remark that the spectral form factor appears in the survival probability for fully ergodic systems [47,48].…”

Section: Discussionmentioning

confidence: 99%

Sensitivity of the spectral form factor to short-range level statistics

2020

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The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behavior is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation can be too restrictive by indicating that the self-correlation imposes a constraint on the spectral form factor integrated over time. More generally, we indicate that each expansion coefficient of the two-point correlation function imposes a constraint on the properly weighted time-integrated spectral form factor. We discuss how these constraints can affect the interpretation of the spectral form factor as a probe for ergodicity. We propose a probe, which eliminates the effect of the constraint imposed by the self-correlation. The use of this probe is demonstrated for a model of randomly incomplete spectra and a Floquet model supporting many-body localization.

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“…17 stimulated a flurry of numerical studies [18][19][20][21] of S N in the Hesenberg model at strong disorder (considered to be deep in the MBL phase), fitting the numerical data by a slow growth of S N ∼ ln ln t (this growth of S N is unrelated to a subleading 22 ∼ ln ln t growth of von-Neumann entropy in a dephasing model of MBL) and arguing that this growth is unbounded which would challenge the established MBL phenomenology, specifically no particle transport in the localized phase. A subsequent study focusing on the steady-state saturation value of S N on the other hand concluded 23 that there are no signs of ergodicity and that S N is compatible with MBL.…”

Section: Introductionmentioning

confidence: 99%

Theory of growth of number entropy in disordered systems

Ghosh,

Žnidarič

2021

Preprint

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We study the growth of the number entropy SN in one-dimensional number-conserving interacting systems with strong disorder, which are believed to display many-body localization. Recently a slow and small growth of SN has been numerically reported, which, if holding at asymptotically long times in the thermodynamic limit, would imply ergodicity and therefore the absence of true localization. By numerically studying SN in the disordered isotropic Heisenberg model we first reconfirm that, indeed, there is a small growth of SN. However, we show that such growth is fully compatible with localization. To be specific, using a simple model that accounts for expected rare resonances we can analytically predict several main features of numerically obtained SN: trivial initial growth at short times, a slow power-law (and not ∼ ln ln t) growth at intermediate times, and the scaling of the saturation value of SN with the disorder strength. Because resonances crucially depend on individual disorder realizations, the growth of SN also heavily varies depending on the initial state, and therefore SN and von-Neumann entropy can behave rather differently.

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

Cited by 76 publications

References 44 publications

Particle fluctuations and the failure of simple effective models for many-body localized phases

Particle fluctuations and the failure of simple effective models for many-body localized phases

Sensitivity of the spectral form factor to short-range level statistics

Theory of growth of number entropy in disordered systems

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