Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder

Sarkar, Madhumita; Ghosh, Roopayan; Khaymovich, Ivan M.

doi:10.1103/physrevb.108.l060203

Cited by 5 publications

(5 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We already said that, due to the heavy-tailed distribution of the off-diagonal elements, the convergence of numerical simulations to the thermodynamic limit of the Lévy-RP model is very slow, see also [44]. However, an attempt to verify our analytical prediction can be seen in Fig.…”

Section: Lévy Rosenzweig-porter Modelmentioning

confidence: 77%

“…This statement can be, in principle, generalized to the Erdös-Rényi graphs with random hopping amplitudes and finite fraction p ∼ O(1) of non-zero edges. Statistically non-homogeneous distributions of the on-site disorder (like in [44]) may lead to a zero fraction of multifractal states, but the question if it can lead to the formation of an entire multifractal phase remains open. Another possibility for creating genuine multifractality is adding hopping-term [55] and on-site disorder correlations [56,57].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…one can estimate a probability to find exactly N g i −1+β δα terms of the order of N −α i in a particular realization of the sum as exp{− N g i − N f X (α i ) 2 /2N f X (α i )+1−β δα} which is double-exponentially small in g i , provided g i ̸ = f X (α i ). Thus, neglecting the double-exponentially small contributions, one can write a typical value of the sum as [22,44]…”

Section: Extensive Sums Of Iid Random Variablesmentioning

confidence: 99%

“…These simplifications, again, restrict the applicability of the following results to the non-ergodic delocalized part of the phase diagram. Now, the problem of calculating the spectrum of fractal dimensions of the local density of states ν i (ϵ) appears as a self-consistent problem [31,44,45,47], and below, we show how to solve it using the SFD graphical algebra introduced earlier.…”

Section: Gaussian Rosenzweig-porter Modelmentioning

confidence: 99%

“…Recently, an interest to non-homogeneous (Cantor-set-like) on-site energies distributions has arisen[44,48].…”

mentioning

confidence: 99%

See 4 more Smart Citations

Anatomy of the eigenstates distribution: A quest for a genuine multifractality

Kutlin,

Khaymovich

2024

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

Motivated by a series of recent works, an interest in multifractal phases has risen as they are believed to be present in the Many-Body Localized (MBL) phase and are of high demand in quantum annealing and machine learning. Inspired by the success of the Rosenzweig-Porter (RP) model with Gaussian-distributed hopping elements, several RP-like ensembles with the fat-tailed distributed hopping terms have been proposed, with claims that they host the desired multifractal phase. In the present work, we develop a general (graphical) approach allowing a self-consistent analytical calculation of fractal dimensions for a generic RP model and investigate what features of the RP Hamiltonians can be responsible for the multifractal phase emergence. We conclude that the only feature contributing to a genuine multifractality is the on-site energies’ distribution, meaning that no random matrix model with a statistically homogeneous distribution of diagonal disorder and uncorrelated off-diagonal terms can host a multifractal phase.

show abstract

Section: Lévy Rosenzweig-porter Modelmentioning

confidence: 77%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Extensive Sums Of Iid Random Variablesmentioning

confidence: 99%

Section: Gaussian Rosenzweig-porter Modelmentioning

confidence: 99%

“…Recently, an interest to non-homogeneous (Cantor-set-like) on-site energies distributions has arisen[44,48].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Anatomy of the eigenstates distribution: A quest for a genuine multifractality

Kutlin,

Khaymovich

2024

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

The Rosenzweig–Porter model revisited for the three Wigner–Dyson symmetry classes

Čadež,

Kumar Nandy,

Rosa

et al. 2024

New J. Phys.

View full text Add to dashboard Cite

Interest in the Rosenzweig-Porter model, a parameter-dependent random-matrix model that interpolates between Poisson and Wigner-Dyson (WD) statistics describing the fluctuation properties of the eigenstates of typical quantum systems with regular and chaotic classical dynamics, respectively,, has come up again in recent years in the ﬁeld of many-body quantum chaos. The reason is that the model exhibits parameter ranges in which the eigenvectors are Anderson-localized, non-ergodic (fractal) and ergodic extended, respectively. We present numerical results for all symmetry classes of Dysons threefold way. We analyzed the ﬂuctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the short- and long-range correlations as measures to explore the transition from Poisson to WD statistics. Furthermore, we performed in-depth studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback-Leibler (KL) divergences and the ﬁdelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a ﬁnite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

show abstract

Long-range spectral statistics of the Rosenzweig-Porter model

Buijsman

2024

Phys. Rev. B

View full text Add to dashboard Cite

The Rosenzweig-Porter model is a single-parameter random matrix ensemble that supports an ergodic, fractal, and localized phase. The names of these phases refer to the properties of the (midspectrum) eigenstates. This work focuses on the long-range spectral statistics of the recently introduced unitary equivalent of this model. By numerically studying the Thouless time obtained from the spectral form factor, it is argued that long-range spectral statistics can be used to probe the transition between the ergodic and the fractal phases. The scaling of the Thouless time as a function of the model parameters is found to be similar to the scaling of the spreading width of the eigenstates. Provided that the transition between the fractal and the localized phases can be probed through short-range level statistics, such as the average ratio of consecutive level spacings, this work establishes that spectral statistics are sufficient to probe both transitions present in the phase diagram. Published by the American Physical Society 2024

show abstract

Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder

Cited by 5 publications

References 55 publications

Anatomy of the eigenstates distribution: A quest for a genuine multifractality

Anatomy of the eigenstates distribution: A quest for a genuine multifractality

The Rosenzweig–Porter model revisited for the three Wigner–Dyson symmetry classes

Long-range spectral statistics of the Rosenzweig-Porter model

Contact Info

Product

Resources

About