Hilbert-space fragmentation, multifractality, and many-body localization

Pietracaprina, Francesca; Laflorencie, Nicolas

doi:10.1016/j.aop.2021.168502

Cited by 26 publications

(11 citation statements)

References 47 publications

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“…Participation entropy is directly connected to the concepts of inverse participation ratio (for q = 2) and, calculated as a function of q allows for a multifractal analysis of the wavefunction [131]. Participation entropy scales differently with system size for delocalized and for localized wave-functions thereby playing a critical role in the analysis of Anderson localization transition [3,[132][133][134] and as well as of the MBL transitions [104,109,[135][136][137][138][139]. Interestingly, the participation entropies can be also used to characterize quantum phase transitions [140][141][142][143][144][145][146][147][148][149] and recently have been used to construct order parameter for measurement-induced phase transitions [150].…”

Section: Participation Entropies and Non-ergodicity Volumementioning

confidence: 99%

Universality in Anderson localization on random graphs with varying connectivity

Sierant¹,

Lewenstein²,

Scardicchio³

2022

Preprint

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We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both spectra and eigenstates), together with new finite size scaling and statistical analysis of the graph ensembles, unveils a universal behavior which is described by two simple, integer, scaling exponents. A by-product of such analysis is a reconciliation of the tension between the results of perturbation theory coming from strong disorder and earlier numerical works, which seemed to suggest that there should be a non-ergodic region above a given value of disorder W E which is strictly less than the Anderson localization critical disorder W C , and that of other works which suggest that there is no such region. We find that, although no separate W E exists from W C , the length scale at which fully developed ergodicity is found diverges like |W − W C | −1 , while the critical length over which delocalization develops is ∼ |W − W C | −1/2 . The separation of these two scales at the critical point allows for a true non-ergodic, delocalized region. In addition, by looking at eigenstates and studying leading and sub-leading terms in system size-dependence of participation entropies, we show that the former contain information about the non-ergodicity volume which becomes non-trivial already deep in the delocalized regime. We also discuss the quantitative similarities between the Anderson transition on random graphs and many-body localization transition.

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Section: Participation Entropies and Non-ergodicity Volumementioning

confidence: 99%

Universality in Anderson localization on random graphs with varying connectivity

Sierant¹,

Lewenstein²,

Scardicchio³

2022

Preprint

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show abstract

“…The second direction, arguably more microscopically motivated, has been to study the MBL problem as an unconventional Anderson localization problem [23] on the complex, correlated Fock-space graph of a quantum many-body system [5,18,19,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. While MBL on Fock space is inherently different from conventional Anderson localization on highdimensional graphs, the latter has served as an important inspiration for the former, with regard to both techniques and the scaling laws governing the transition [43][44][45][46][47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

“…While MBL on Fock space is inherently different from conventional Anderson localization on highdimensional graphs, the latter has served as an important inspiration for the former, with regard to both techniques and the scaling laws governing the transition [43][44][45][46][47][48][49][50][51][52]. This direction has led to crucial insights, such as the multifractal scaling of MBL eigenstates on the Fock space [19,26], emergent fragmentation of the Fock space in the MBL phase [18,31,33,34], and the understanding that maximal correlations in the Fockspace disorder are a necessary ingredient for MBL to be stable [37,53].…”

Section: Introductionmentioning

confidence: 99%

Fock-space anatomy of eigenstates across the many-body localization transition

Roy

Logan

2021

Phys. Rev. B

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“…This result may seem surprising. Indeed, the analogy between the MBL transition and the Anderson transition on random graphs is not consensual with some differences pointed out in the literature [28,33,[52][53][54][55]. In the case of the MBL transition, it is known that the phenomenological RG predictions are extremely difficult (some studies even claim impossible [56]) to verify numerically [57,58].…”

Section: Introductionmentioning

confidence: 99%

Critical properties of the Anderson transition on random graphs: Two-parameter scaling theory, Kosterlitz-Thouless type flow, and many-body localization

et al. 2022

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In this paper, we investigate the Anderson transition on random graphs by taking advantage of the knowledge on MBL. The numerous studies on the MBL transition, and in particular the difficulty of describing this phenomenon analytically starting from a microscopic model, have led to the development of an approach called the phenomenological renormalization group (RG) [46][47][48][49][50]. This approach is based on an avalanche mechanism thought to be responsible for an instability of MBL leading to a transition to a thermal phase [42,51]. The phenomenological RG allows to describe the renormalization flow in the vicinity of the MBL transition. Remarkably, recent studies have shown that this flow is of the Kosterlitz-Thouless type [48] (or at least very similar to it [50]). Thus, from the MBL side, we have precise analytical predictions of the flow and the nature of the transition. This is not the case for the Anderson transition on random graphs: although several critical properties are known, the flow and nature of the transition are not. The purpose of this paper is to remedy this. We will show that the flow of the Anderson transition is of Kosterlitz-Thouless type, extremely similar to the MBL transition,

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Hilbert-space fragmentation, multifractality, and many-body localization

Cited by 26 publications

References 47 publications

Universality in Anderson localization on random graphs with varying connectivity

Universality in Anderson localization on random graphs with varying connectivity

Fock-space anatomy of eigenstates across the many-body localization transition

Critical properties of the Anderson transition on random graphs: Two-parameter scaling theory, Kosterlitz-Thouless type flow, and many-body localization

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