Entanglement critical length at the many-body localization transition

Pietracaprina, Francesca; Parisi, Giorgio; Mariano, A.; Pascazio, Saverio; Scardicchio, Antonello

doi:10.1088/1742-5468/aa9338

Cited by 28 publications

(23 citation statements)

References 56 publications

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“…are functions of L/ξ, where L is the system size. The collapse thus obtained is usually quite good (see for example [35,40,41]) but the critical exponents contradict simple bounds set by general considerations [42]: numerical works find ν 1, while the arguments in Ref. [42] would imply ν ≥ 2.…”

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confidence: 88%

Can we study the many-body localisation transition?

Panda

Scardicchio

Schulz

et al. 2020

EPL

189

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PACS 74.62.En -Effects of disorder PACS 64.60.an -Finite-size systems (General studies of phase transitions) PACS 72.15.Rn -Localization effects (Anderson or weak localization)Abstract -We present a detailed analysis of the length-and timescales needed to approach the critical region of MBL from the delocalised phase, studying both eigenstates and the time evolution of an initial state. For the eigenstates we show that in the delocalised region there is a single length, which is a function of disorder strength, controlling the finite-size flow. Small systems look localised, and only for larger systems do resonances develop which restore ergodicity in the form of the eigenstate thermalisation hypothesis. For the transport properties, we study the time necessary to transport a single spin across a domain wall, showing how this grows quickly with increasing disorder, and compare it with the Heisenberg time. For a sufficiently large system the Heisenberg time is always larger than the transport time, but for a smaller system this is not necessarily the case. We conclude that the properties of the MBL transition cannot be explored using the system sizes or times available to current numerical and experimental studies.

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confidence: 88%

Can we study the many-body localisation transition?

Panda

Scardicchio

Schulz

et al. 2020

EPL

189

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“…Entanglement entropies can be extracted from entanglement spectra [14,15]. An entanglement spectrum encodes statistics beyond the entanglement entropy [16], of which several have been studied in the context of MBL [17][18][19][20][21][22][23]. The physical information encoded in the entanglement spectrum of a many-body localized eigenstate is almost fully carried by the smallest few elements [19], indicating the potential physical significance of the extreme value statistics [24].…”

Section: Introductionmentioning

confidence: 99%

Gumbel statistics for entanglement spectra of many-body localized eigenstates

2019

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An entanglement spectrum encodes statistics beyond the entanglement entropy, of which several have been studied in the context of many-body localization. We numerically study the extreme value statistics of entanglement spectra of many-body localized eigenstates. The physical information encoded in these spectra is almost fully carried by the smallest few elements, suggesting the extreme value statistics to have physical significance. We report the surprising observation of Gumbel statistics. Our result provides an analytical, parameter-free characterization of many-body localized eigenstates.

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“…In this work we analyze the thermal-MBL transition through a new lens, that of the eigenstate entanglement spectrum (EES) [41][42][43][44][45][46]. The EES contains far more information about the pattern of quantum entanglement than the EEE (and it may be experimentally observable [47]).…”

Section: Introductionmentioning

confidence: 99%

Characterizing the many-body localization transition using the entanglement spectrum

2017

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We numerically explore the many body localization (MBL) transition through the lens of the entanglement spectrum. While a direct transition from localization to thermalization is believed to be obtained in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate 'quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical lower bound on the critical disorder strength for MBL. A careful analysis of the high energy part of the entanglement spectrum (which contains universal information about the critical point) allows us to study the crossover from criticality to MBL, and we find evidence for such a crossover which could allow us to place a numerical upper bound on the critical disorder strength for MBL.

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Entanglement critical length at the many-body localization transition

Cited by 28 publications

References 56 publications

Can we study the many-body localisation transition?

Can we study the many-body localisation transition?

Gumbel statistics for entanglement spectra of many-body localized eigenstates

Characterizing the many-body localization transition using the entanglement spectrum

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