Pith. sign in

REVIEW 4 cited by

Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2002.02979 v2 pith:C4KEXCOO submitted 2020-02-07 cond-mat.dis-nn cond-mat.quant-gas

V. E. Kravtsov , I. M. Khaymovich , B. L. Altshuler , L. B. Ioffe This is my paper
classification cond-mat.dis-nncond-mat.quant-gas
keywords modelphaserandomln-rpmatrixmultifractalpointtransition
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase and ergodic transition have a status of a mathematical theorem. Yet, this phase in GRP model is oversimplified: the spectrum of fractal dimensions is degenerate and the mini-band in the local spectrum is not multifractal. In this paper we suggest an extension of the GRP model by adopting a logarithmically-normal (LN) distribution of off-diagonal matrix elements. A family of such LN-RP models is parametrized by a symmetry parameter $p$ and it interpolates between the GRP at $p\rightarrow 0$ and Levy ensembles at $p\rightarrow\infty$. A special point $p=1$ is shown to be the simplest approximation to the Anderson localization model on a random regular graph.We study in detail the phase diagram of LN-RP model and show that $p=1$ is a tricritical point where the multifractal phase first collapses. This collapse is shown to be unstable with respect to the truncation of the log-normal distribution. We suggest a new criteria of stability of the non-ergodic phases and prove that the Anderson transition in LN-RP model is discontinuous at all $p>0$.

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Circular Rosenzweig-Porter random matrix ensemble

    cond-mat.dis-nn 2021-11 unverdicted novelty 7.0 of 10

    A unitary analogue of the Rosenzweig-Porter ensemble is defined through Dyson Brownian motion and shown numerically to share eigenvalue and eigenstate statistics with the original ensemble.

  2. Level statistics in the fractal phase of generalized Rosenzweig--Porter models

    cond-mat.dis-nn 2026-07 accept novelty 6.0 of 10

    Full counting statistics of generalized Rosenzweig-Porter models collapse onto a universal scaling function of E/E_T in the fractal phase, confirmed by free-probability/replica analytics and large-deviation numerics, ...

  3. Resonance Proliferation Across Localization Transitions

    cond-mat.dis-nn 2026-05 unverdicted novelty 6.0 of 10

    A flow equation for the resonance density exponent θ(w) derived in the SJA predicts resonance proliferation driving delocalization, with θ(w)>0 for localized phases and instability signaling thermalization, matching n...

  4. Spectral Transitions of the Entanglement Hamiltonian in Monitored Free Fermions

    quant-ph 2025-09 conditional novelty 6.0 of 10

    Spectral statistics of the entanglement Hamiltonian reveal a sharp ergodic-to-non-ergodic transition in monitored free fermions at gamma_c approx 5.16, with critical exponent nu approx 0.86, and hint at a possible int...

Pith tools