Localization to ergodic transitions: is Rosenzweig–Porter ensemble the hidden skeleton?

Shukla, Pragya

doi:10.1088/1367-2630/18/2/021004

Cited by 27 publications

(23 citation statements)

References 27 publications

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“…Examining the bulk and the tail of level spacing distribution together with the number variance we have demonstrated that the proposed models of spectral statistics in MBL crossover [35,36,38,39] grasp level statistics accurately only at the level of few of level spacings. To reproduce broad distributions of the sample averaged gap ratio r S in the MBL transition we have introducted the wSRPM that is a statistical mixture of the well known family of short-range plasma models.…”

Section: Conclusion and Beyondmentioning

confidence: 98%

“…Another work [38] suggest that Rosenzweig-Porter (RP) ensemble can be appropriate to describe the MBL transition. Multifractal properties of eigenvectors of this model, which is defined as an ensemble of real symmetric (for β = 1 orthogonal class relevant for us) random matrices M = (M ij ) of size n × n with matrix elements being independent Gaussian variables with zero average values M ij = 0 and M 2 ii = 1, and…”

Section: Level Statistics In Mbl Transitionmentioning

confidence: 99%

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Level statistics across the many-body localization transition

Sierant

Zakrzewski

2019

Phys. Rev. B

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Level statistics of systems that undergo many-body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter-and intra-sample randomness allows us to pin point differences between transitions in random and quasi-random disorder, showing the effects due to Griffiths rare events for the former case. It is argued that the transition in the case of random disorder exhibits universal features that are identified by constructing an appropriate model of intermediate spectral statistics which is a generalization of the family of short-range plasma models. The considered weighted short-range plasma model yields a very good agreement both for level spacing distribution including its exponential tail and the number variance up to tens of level spacings outperforming previously proposed models. In particular, our model grasps the critical level statistics which arise at disorder strength for which the inter-sample fluctuations are the strongest. Going beyond the paradigmatic examples of many-body localization in spin systems, we show that the considered model also grasps the level statistics of disordered Bose-and Fermi-Hubbard models. The remaining deviations for long-range spectral correlations are discussed and attributed mainly to the intricacies of level unfolding.

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Section: Conclusion and Beyondmentioning

confidence: 98%

Section: Level Statistics In Mbl Transitionmentioning

confidence: 99%

Level statistics across the many-body localization transition

Sierant

Zakrzewski

2019

Phys. Rev. B

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“…As confirmed by a large number of theoretical, numerical as well as experimental studies of wide-ranging complex systems [5,6,22,29], Poisson and GOE type behavior of the spectral statistics are indicators of localized and delocalized dynamics of the eigenfunctions, respectively, with an intermediate statistics indicating partially localized states [38]; (note, as discussed in [37], the above relation between spectral statistics and eigenfunction dynamics is valid only for Hermitian matrices). This implies that, for w ∼ 10 parametric Gaussian ensemble and the expressions for Y and Λ e for them can be easily obtained (see [19], [28] and [20] for details). The two ensembles can briefly be described as follows.…”

Section: Transition In a Flat Band With Other Bands In The Neigh-mentioning

confidence: 99%

“…The mapping not only implies connections of the flat band statistics with the BE but also with other complex systems under similar global constraints e.g. symmetry conditions and conservation laws [27,28]. Additionally, as discussed in detail in [15], it also leads to a single parametric formulation of the level density and inverse participation ratio of the perturbed flat band.…”

Section: Introductionmentioning

confidence: 98%

Disorder perturbed flat bands. II. Search for criticality

Shukla

2018

Phys. Rev. B

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We present a common mathematical formulation of the level statistics of a disordered tightbinding lattice, with one or many flat bands in clean limit, in which system specific details enters through a single parameter. The formulation, applicable to both single as well as many particle flat bands, indicates the possibility of two different types of critical statistics: one in weak disorder regime (below a system specific disorder strength) and insensitive of the disorder-strength, another in strong disorder regime and occurs at specific critical disorder strengths. The single parametric dependence however relates the statistics in the two regimes (notwithstanding different scattering conditions therein). This also helps in revealing an underlying universality of the statistics in weakly disordered flat bands, shared by a wide-range of other complex systems irrespective of the origin of their complexity.

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“…Recent results indicate that it may be characterized by a Griffiths-like phase in which anomalously different disorder regions seem to dominate the dynamics [33][34][35]55]; nonetheless, the debate is still open [56]. To describe the flow of intermediate statistics observed in this region, mean-field plasma models with effective power-law interactions between energy levels [24,57], the Rosenzweig-Porter ensemble with multifractal eigenvectors [58,59], a family of short-range plasma models [60] and generalizations [42,43] have been used. Finally, for disorder strengths larger than a critical value that is dependent on the dimension of the Hilbert space, the chain gradually reaches the MBL phase.…”

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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Localization to ergodic transitions: is Rosenzweig–Porter ensemble the hidden skeleton?

Cited by 27 publications

References 27 publications

Level statistics across the many-body localization transition

Level statistics across the many-body localization transition

Disorder perturbed flat bands. II. Search for criticality

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

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