Non-ergodic delocalization in the Rosenzweig–Porter model

Soosten, Per von; Warzel, Simone

doi:10.1007/s11005-018-1131-7

Cited by 59 publications

(49 citation statements)

References 20 publications

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“…This approximation works well for the full random matrix Hamiltonian (coordination number N → ∞) and fails for the sparse hopping matrix like in the initial Hamiltonian of the Anderson model on RRG (finite coordination number K + 1). The situation here is similar to the perturbative derivation of multifractality in the Gaussian RP model [25] which appeared to be exact [26,27]. That is why one should first derive the RP model equivalent to the short-range sparse problem and then apply the Wigner-Weisskopf approximation to this RP model.…”

Section: Localization Ergodic and Fully-weakly Ergodic Transitionsmentioning

confidence: 74%

Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

Khaymovich

Kravtsov

2021

SciPost Phys.

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We consider the static and the dynamical phases in a Rosenzweig-Porter (RP) random matrix ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the averaged survival probability may decay with time as a simple exponent, as a stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. As an example, we consider the mapping of the Anderson localization model on Random Regular Graph onto the RP model and find exact values of the stretch-exponent \kappaκ in the thermodynamic limit. As another example we consider the logarithmically-normal RP random matrix ensemble and find analytically its phase diagram and the exponent \kappaκ. Our theory allows to describe analytically the finite-size multifractality and to compute the critical length with the exponent \nu_{MF}=1νMF=1 associated with it.

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Section: Localization Ergodic and Fully-weakly Ergodic Transitionsmentioning

confidence: 74%

Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

Khaymovich

Kravtsov

2021

SciPost Phys.

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“…Remarkably, this multifractality exists in a finite range of parameters and thence requires no fine-tuning, while the states nonetheless show anomalous algebraic multifractal correlations similar-in some but not all-respects to the critical ones [29][30][31][32][33]. We present an effective random matrix Hamiltonian, which captures the numerically obtained multifractality remarkably well, bearing a family resemblance to the Rosenzweig-Porter random matrix ensemble [34], generalisations of which are known to host multifractal eigenstates [9,11,[35][36][37][38][39][40].…”

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confidence: 83%

Multifractality without fine-tuning in a Floquet quasiperiodic chain

et al. 2018

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Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band of multifractal wavefunctions in a periodically driven chain of non-interacting particles subject to spatially quasiperiodic disorder. Remarkably, this multifractality is robust in that it does not require any fine-tuning of the model parameters, which sets it apart from the known multifractality of critical wavefunctions. The multifractality arises as the periodic drive hybridises the localised and delocalised sectors of the undriven spectrum. We account for this phenomenon in a simple random matrix based theory. Finally, we discuss dynamical signatures of the multifractal states, which should betray their presence in cold atom experiments. Such a simple yet robust realisation of multifractality could advance this so far elusive phenomenon towards applications, such as the proposed disorder-induced enhancement of a superfluid transition.

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“…In order to proceed, in the full-ranked version of our model (1) we use the analogy between the recursive representation (19) and the one of the Dyson Brownian motion (17). Indeed, like in the Dyson Brownian motion, one can consider a stochastic random matrix process over auxiliary time, 0 ≤ t ≤ 1, defined as a ∆t → 0 limit of the recursion (20a)…”

Section: Dyson-brownian-motion-like Stochastic Process For Tirp: β =mentioning

confidence: 99%

“…However, the only random-matrix platform known so far to show robust fractal [14][15][16][17][18][19][20][21] or multifractal [22][23][24] properties is the family of the so-called Rosenzweig-Porter (RP) ensembles [25] and some Floquet-driven systems [26][27][28] showing the same effective Floquet Hamiltonian. All these models are inevitably long-range and given by the complete graphs with different statistical properties of on-site (diagonal) disorder and matrix hopping terms.…”

Section: Introductionmentioning

confidence: 99%

Emergent fractal phase in energy stratified random models

Kutlin

Khaymovich

2021

SciPost Phys.

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We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson’s model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.

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Non-ergodic delocalization in the Rosenzweig–Porter model

Cited by 59 publications

References 20 publications

Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

Multifractality without fine-tuning in a Floquet quasiperiodic chain

Emergent fractal phase in energy stratified random models

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