Criterion for the occurrence of many-body localization in the presence of a single-particle mobility edge

Modak, Ranjan; Ghosh, Soumi; Mukerjee, Subroto

doi:10.1103/physrevb.97.104204

Cited by 29 publications

(31 citation statements)

References 49 publications

(74 reference statements)

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“…Moreover, in both sides of a = 1, transition between different P s phases are clearly visible. The volume law of eigenstate EE has also been recently observed for 1D short-range noninteracting model in the presence of correlated disorder, where there exists a mobility edge in single particle spectrum [65,66].…”

Section: Entanglement Entropy(ee)mentioning

confidence: 59%

Many-body dynamics in long-range hopping models in the presence of correlated and uncorrelated disorder

Modak

Nag

2020

Phys. Rev. Research

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Much have been learned about universal properties of entanglement entropy (EE) and participation ration (PR) for Anderson localization. We find a new sub-extensive scaling with system size of the above measures for algebraic localization as noticed in one-dimensional long-range hopping models in the presence of uncorrelated disorder. While the scaling exponent of EE seems to vary universally with the long distance localization exponent of single particle states (SPSs), PR does not show such university as it also depends on the short range correlations of SPSs. On the other hand, in presence of correlated disorder, an admixture of two species of SPSs (ergodic delocalized and non-ergodic multifractal or localized) are observed, which leads to extensive (sub-extensive) scaling of EE (PR). Considering typical many-body eigenstates, we obtain above results that are further corroborated with the asymptotic dynamics. Additionally, a finite time secondary slow growth in EE is witnessed only for correlated case while for uncorrelated case there exists only primary growth followd by the saturation. We believe that our findings from typical many-body eigenstate would remain unaltered even in the weakly interacting limit.

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Section: Entanglement Entropy(ee)mentioning

confidence: 59%

Many-body dynamics in long-range hopping models in the presence of correlated and uncorrelated disorder

Modak

Nag

2020

Phys. Rev. Research

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“…The existence of a many-body intermediate phase (MBIP, marked in gray) is highly debated. MBL in some cases, but not in others [13,41]. Definite conclusions, however, are often challenged by finite-size effects.…”

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confidence: 99%

Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge

et al. 2019

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We experimentally study many-body localization (MBL) with ultracold atoms in a weak onedimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL, when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase.arXiv:1809.04055v3 [cond-mat.quant-gas]

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“…In the presence of interactions these models also undergo transitions from thermal to athermal phases [30,31]. However, it has been argued that these models are different from those without single-particle mobility edges in that they possess a nonergodic extended phase at the intermediate potential strengths.…”

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confidence: 99%

Transport in the nonergodic extended phase of interacting quasiperiodic systems

2020

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We study the transport properties and the spectral statistics of a one-dimensional closed quantum system of interacting spinless fermions in a quasiperiodic potential which produces a single-particle mobility edge in the absence of interaction. For such systems, it has been shown that the many-body eigenstates can be of three different kinds: extended and eigenstate thermalization hypothesis (ETH) obeying (thermal), localized and ETH violating (many body localized), and extended and ETH violating (nonergodic extended). Here we investigate the nonergodic extended phase from the point of view of level spacing statistics and charge transport. We calculate the dc conductivity and the low-frequency conductivity σ (ω) and show that both are consistent with subdiffusive transport. This is contrasted with diffusive transport in the thermal phase and blocked transport in the MBL phase.

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Criterion for the occurrence of many-body localization in the presence of a single-particle mobility edge

Cited by 29 publications

References 49 publications

Many-body dynamics in long-range hopping models in the presence of correlated and uncorrelated disorder

Many-body dynamics in long-range hopping models in the presence of correlated and uncorrelated disorder

Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge

Transport in the nonergodic extended phase of interacting quasiperiodic systems

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