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REVIEW 4 major objections 4 minor 52 references

L\'evy Sachdev-Ye-Kitaev Model

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that the 4-fermion Sachdev-Ye-Kitaev (SYK) model with couplings drawn from a fat-tailed L\'evy stable distribution crosses over from chaotic to integrable spectral correlations as the stability index $\mu$ decreases…

desk verdict A novel fat-tailed SYK variant with a plausible chaotic-to-integrable crossover, but the analytic crossover bound is not sharp and the numerics lack error bars; still worth refereeing. read the letter →

arxiv 2506.04343 v1 pith:EEITLFY7 submitted 2025-06-04 quant-ph cond-mat.stat-mechcond-mat.str-elhep-th

Budhaditya Bhattacharjee , William E. Salazar , Dario Rosa , Alexei Andreanov This is my paper
classification quant-phcond-mat.stat-mechcond-mat.str-elhep-th PACS 05.45.Mt
keywords Sachdev-Ye-KitaevmodelL\'evystabledistributionmany-bodyquantumchaoslevelspacingratiospectralformfactormultifractalspectrumcrossovertointegrabilityrandommatrixtheory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that replacing the Gaussian disorder of the 4-fermion SYK model with fat-tailed L\'evy-stable couplings leaves the bulk spectral statistics chaotic down to a stability index $\mu_c$ that vanishes as $N\to\infty$, and only then lets integrable correlations take over. The effect is a many-body crossover: the location $\mu_c\sim N^{-1}$ for short-range statistics and $\mu_{c,2}\sim N^{-1.63}$ for long-range statistics is set by a competition between the number of interaction terms and the exponentially large Hilbert-space dimension, not by the $\mu=1$ mobility edge of a single L\'evy random matrix. If correct, the L\'evy SYK model is a solvable all-to-all model whose spectral correlations interpolate between random-matrix chaos and integrability without extra structure such as sparsity.

What carries the argument

The load-bearing object is the L\'evy hierarchy: a sample of $\mathcal N$ L\'evy-stable variables contains $O(\mathcal N^{1-z})$ terms of magnitude $O(\mathcal N^{1/\mu}\mathcal N^{(z-1)/\mu})$ for $0\le z\le1$, meaning $O(1)$ outliers of size $\mathcal N^{1/\mu}$, $O(\mathcal N)$ mid-size terms of order one, and a dense weak background. The paper uses this hierarchy to decompose the Hamiltonian into commuting bubble sectors, then applies a resonance-counting criterion: chaotic statistics survive while the typical coupling $j_{\rm typ}$ exceeds the mean level spacing $\Delta_\pm$ inside a bubble, and integrable statistics set in when $j_{\rm typ}\ll\Delta_\pm$. The multifractal spectrum of fractal dimensions $f_L(\alpha)=\mu\alpha\,\theta(1-\mu\alpha)+(1/\mu+1-\alpha)\theta(\mu\alpha-1)$, with fusion rules for sums, squares and ratios of L\'evy variables, converts this criterion into the estimate $\mu_c\sim \ln N/N$. The exponential-vs-polynomial competition between Hilbert-space dimension $D\sim2^{N/2}$ and the number of couplings $\mathcal N\sim N^4$ is what makes the crossover a many-body effect rather than a single-particle one.

What would settle it

Compute the full nearest-neighbour spacing distribution $P(s)$ inside a single bubble (not just the averaged $\langle r\rangle$) for system sizes $N=26$\textendash$32$ at $\mu$ near the predicted $\mu_c$. If $P(s)$ is Poisson while the typical spacing is still much larger than the typical coupling, but rare near-degeneracies control the level statistics, the resonance-counting criterion is wrong; alternatively, if including third-order perturbative corrections changes the extracted exponent $\eta_1$, the second-order bubble picture is incomplete.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the spectrum of the L\'evy SYK model splits into blocks (\'\'bubbles\'\') generated by the $O(1)$ parametrically large couplings, and that inside a block the typical coupling strength decays polynomially with $N$ while the mean level spacing decays exponentially. Integrable spectral correlations appear when the typical coupling becomes much smaller than the mean spacing, which happens for $\mu\lesssim \ln N/N$; numerically this shows up as $\mu_c\sim N^{-\eta_1}$ with $\eta_1\approx1$ for short-range statistics and $\mu_{c,2}\sim N^{-\eta_2}$ with $\eta_2\approx1.63$ for long-range statistics. The same data show that edge statistics, controlled by the extreme eigenvalues, follow the single-particle L\'evy mobility edge at $\mu\approx1$. The paper therefore claims a qualitative separation: the bulk crossover is a many-body phenomenon, the edge statistics are not.

Load-bearing premise

The paper's prediction rests on the resonance-counting criterion in the supplementary (Eqs. (54)\textendash(56)): integrable statistics set in when the typical coupling is much smaller than the mean level spacing inside a block, with that spacing estimated by replacing each eigenvalue difference by its typical multifractal value; if rare large fluctuations in the spacings dominate, or if higher-order terms mix the blocks, the predicted $\mu_c\sim\ln N/N$ scaling fails.

Editorial extensions

If this is right

  • For any fixed $\mu>0$, the bulk spectrum of LSYK becomes Gaussian random-matrix-like in the thermodynamic limit, so the chaotic-to-integrable change is a crossover that recedes as $N\to\infty$, not a sharp transition.
  • Long-range spectral correlations (the spectral-form-factor ramp) survive stronger L\'evy disorder than short-range ones, since $\eta_2>\eta_1$; different probes therefore define different crossover values.
  • Edge statistics, including the ground-state energy and the gap ratio, are controlled by the single-particle L\'evy mobility edge at $\mu\approx1$ rather than by the bulk crossover.
  • If $q$ is taken to scale with $N$ so that the number of couplings is comparable to the Hilbert-space dimension, the crossover should sharpen into a true many-body transition at an $N$-independent value of $\mu$.
  • The model is expected to remain solvable in the large-$N$ SYK sense, so the claimed crossover should be accessible to analytic techniques for L\'evy spin glasses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The two distinct exponents $\eta_1\approx1$ and $\eta_2\approx1.63$ suggest that other spectral probes, such as number variance or spectral rigidity, might reveal a family of crossover exponents; the paper does not test this.
  • Because the bubble decomposition is set by only $O(1)$ largest couplings, the crossover should be visible in individual disorder realizations; checking realization-to-realization fluctuations of $\langle r\rangle$ near $\mu_c$ would test whether the ensemble average hides a sharp per-sample transition.
  • If the double-scaled limit $q\sim N$ realizes the predicted $N$-independent transition, the critical value would be a tunable constant, giving a many-body analogue of the L\'evy mobility edge; this is a concrete target for future numerics.
  • The paper's solvability claim suggests the crossover might be probed analytically through a large-$N$ saddle point of the L\'evy-disorder partition function; comparing such a calculation with the numerically extracted exponents would be a sharp test of the bubble picture.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper studies the q=4 Majorana SYK model with couplings drawn from a symmetric Lévy stable distribution of index μ∈(0,2]. Using exact diagonalization up to N=32 fermions, it reports that the nearest-neighbor r-ratio and the spectral form factor deviate from Gaussian RMT behavior below a system-size-dependent crossover value μ_c that scales as N^{-η1} with η1≈1 for short-range statistics and as N^{-η2} with η2≈1.63 for long-range statistics. The density of states splits into 'bubbles' controlled by the few parametrically large outlier couplings. The paper attributes this to a many-body mechanism distinct from the single-particle Lévy mobility edge at μ=1, which it sees separately in the edge statistics. A supplemental multifractal/fusion-rule analysis leads to a resonance-counting criterion j_typ ≪ Δ± and predicts μ_c ≲ ln N/N.

Significance. If correct, the paper would establish a genuinely many-body spectral crossover in an all-to-all disordered fermion model without added structure: for any fixed μ>0 the model is RMT-like in the thermodynamic limit, yet at finite N it crosses over to integrable spectral correlations as the disorder becomes fat-tailed. This is a useful contrast to sparse SYK and Lévy random matrices, and the SFD-based hierarchy method is an ambitious attempt to make the crossover analytically tractable. The paper also makes concrete falsifiable predictions: the two exponents η1 and η2, and the hierarchy/bubble picture, which is directly visible in the density of states. However, the analytic derivation currently contains a sign error and an uncontrolled typical-value replacement, and the numerical exponents lack error bars and threshold consistency; these issues must be resolved before the quantitative claims can be accepted.

major comments (4)
  1. [Supplement, Eq. (55)] The inequality in Eq. (55) has the Hilbert-space factor on the wrong side. From N^{-q/μ} ≲ N^{q c/μ} N^{N ln 2/ln N}, multiplying by N^{q/μ} yields 1 ≲ N^{q(1+c)/μ} N^{N ln 2/ln N}, which is trivially true for all μ and cannot lead to Eq. (56). The intended comparison j_typ ≪ Σ e_k/D^2 requires the factor N^{N ln 2/ln N} in the denominator, i.e. N^{-q/μ} ≲ N^{q c/μ} N^{-N ln 2/ln N}; only then does one obtain μ ≲ q(1+c) ln N/(N ln 2). This sign/placement error is load-bearing because Eq. (56) is the paper's analytic crossover prediction.
  2. [Supplement, Eqs. (54)–(56)] The resonance-counting criterion is not controlled. Eq. (54) identifies integrability with j_typ ≪ Δ±, and the estimate of Δ± replaces each spacing e_k by its typical value N^{-α0} before reinserting stable-law growth. For μ<2, sums of Lévy variables are fixed by rare large terms rather than by the typical term; the paper uses exactly this fact for the total interaction strength in Eq. (14). Since the SFD f_Δ is broad, rare large spacings can dominate the mean spacing, so the condition j_typ ≪ Δ± may be met at a value of μ that differs from Eq. (56) by powers of N. No independent computation of the full level-spacing distribution is provided to test this replacement. This gap directly weakens the claimed analytic explanation of η1≈1.
  3. [Main text Fig. 3 and Supplement Eq. (5)] The threshold used to define μ_c differs by an order of magnitude between the main text and the supplement: roughly 10% deviation in the main text versus 1% in the supplement Eq. (5). No error bars, disorder-realization counts, or fit qualities are reported for the slopes in Figs. 3 and 7, and the supplement itself gives 1.1≤η2≤1.7, a wide range. The quantitative claims η1≈1, η2≈1.63, and η2≳η1 are therefore not established to the precision used in Eqs. (6) and (9); the current evidence supports only an order-of-magnitude crossover.
  4. [Main text Eq. (6) and Supplement Eq. (56)] The analytic prediction is an upper bound μ ≲ ln N/N, while the numerical result is μ_c ~ N^{-1}. For the accessible sizes N=14–32, ln N/N exceeds N^{-1} by a factor of about 3–4, so the data cannot distinguish a logarithmic correction from a pure power law; the agreement is order-of-magnitude only. Given that the prefactors a′, b, and c are free O(1) coefficients, the comparison in Eq. (56) is not a sharp test of the predicted scaling unless the prefactor is computed or a larger range of N is studied.
minor comments (4)
  1. [Main text, Eqs. (6)–(7) and Fig. 6] Equation (6) should read ln μ_c = -η1 ln N rather than μ_c = -η1 ln N, and Eq. (7) describes exponential decay in N, so the Fig. 6 caption's 'weak power-law' wording should be corrected.
  2. [Main text, Fig. 5 and Supplement, SFF section] The main text and the supplement disagree about whether the peak/bump appears in the connected or disconnected SFF: Fig. 5 is labeled 'Connected SFF' but the text speaks of the disconnected SFF, and the supplement states the peak is absent in the full SFF and appears in the disconnected part. This should be reconciled because the scaling of τ* is a central observable.
  3. [Main text and Supplement, notation] The symbol N is used both for the number of fermions and for the number of couplings binom(N,q), particularly in Eqs. (54)–(56) of the supplement; distinct notation would make the powers of N and the logarithm much easier to follow.
  4. [Supplement, Eq. (8)] Equation (8) is written as if the tail approximation P(x)=γ(μ)σ/|x|^{μ+1} held for all x; it should be stated explicitly that this is the asymptotic large-x form, since the later analysis uses it in estimating counts and sums.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the numerical crossovers are measured independently, and the analytic bound follows from the stated Lévy-hierarchy assumptions rather than from the fitted exponents.

full rationale

The paper's central quantitative claims are numerical: μ_c is read off from exact-diagonalization ⟨r⟩ data as the 10% deviation point from the RMT value (Eq. (6), Fig. 3), and μ_{c,2} is extracted from the extrapolation α_μ→0 in the Thouless-time analysis (Eq. (9), Fig. 7). Neither extraction uses the analytical hierarchy argument as an input, so these are independent measurements, not predictions forced by a fit. The analytical argument in the Supplement builds the SFD hierarchy from the Lévy tail and order statistics (Eqs. (8)-(13)), then imposes an explicit resonance condition, j_typ ≪ Δ_± (Eq. (54)). This criterion is heuristic, and the estimate of Σ e_k by the typical value N^{-α0} is a modeling approximation that may be questioned on rare-event grounds, but no measured crossover exponent enters Eqs. (54)-(56). The final bound μ ≲ ln N/N is compared to the numerics only as a consistency check: the paper says the measured μ_c ~ 1/N is "consistent with the bound (56)", and footnote 4 explicitly flags the logarithmic factor as "possibly an artefact of the multi-fractal analysis". Thus the bound is not constructed to reproduce the measured exponent. The self-citations in the bibliography (Refs. [11,44]) concern numerical techniques such as Chebyshev filtering and are not load-bearing for the spectral-crossover claim. The remaining concern about rare-event dominance in Lévy sums is a correctness question about the typical-value replacement, not a circular reduction of the prediction to its inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central numerical claims use only standard disorder-averaged spectral probes, but the explanation of the crossover relies on the Lévy hierarchy plus an author-proposed resonance criterion with free O(1) constants. The edge-statistics interpretation imports the known single-particle Lévy mobility edge. No new particles, forces, or entities are introduced; the bubbles are emergent sectors of the spectrum.

free parameters (5)
  • η1 (short-range crossover exponent) = ~1 (slope of log μ_c vs log N)
    Fitted from the N-dependence of the r-ratio crossover μ_c, defined by a 10% (main text) or 1% (supplementary) deviation from RMT. No error bars are quoted.
  • η2 (long-range crossover exponent) = ~1.63 in main text; 1.1-1.7 in supplementary
    Fitted from the N-dependence of μ_{c,2} where the Thouless time approaches O(1); the paper itself calls this an order-of-magnitude estimate.
  • α* (SFF peak time exponent) = 0.15
    Exponent in log10 τ* ~ -0.15 N for the maximum of the connected SFF (Eq. 7).
  • a' = a + b (resonance-counting coefficients) = undetermined, O(1)
    In Eq. (5) the predicted crossover is μ_c ~ a' ln N/(N ln 2); the coefficients a and b are stated to be O(1) functions of q but never computed, so the prefactor of the predicted scaling is free.
  • b (extensive-sum exponent in SFD analysis) = assumed in (0,1), not computed
    Determines the shift β of the sum-of-squares SFD f_S and the final bound μ ≲ ln N/((q c + q) N ln 2) with c = 1 - min{1, 2(1-b)}; the comparison with numerics is insensitive to b only at the level of the exponent.
assumptions (6)
  • standard math Lévy stable distributions with index μ<2 have the asymptotic power-law tail P(x) ~ γ(μ)σ/|x|^{μ+1}.
    Used in the supplementary to derive the Lévy hierarchy and the SFD f_L; standard result from Gnedenko-Kolmogorov and Nolan.
  • domain assumption The 'Lévy Hierarchy' theorem: O(N^{1-z}) sampled variables have magnitude O(N^{(z-1)/μ}) for 0≤z≤1.
    Stated in the main text and proved in the supplementary by counting the tail of the Lévy distribution; it underlies the bubble-splitting picture and all subsequent SFD estimates.
  • domain assumption Multifractal fusion rules [52] apply to sums, squares, and ratios of Lévy random variables.
    Transfers the statistics of single random variables to the eigenvalue differences of the many-body Hamiltonian; this is the main analytical engine of the paper, used in Eqs. (26)-(48) of the supplementary.
  • ad hoc to paper Integrable spectral statistics set in when the typical coupling satisfies j_typ ≪ Δ_±, with Δ_± estimated from the typical value of the eigenvalue-difference SFD.
    Proposed in Eq. (54) of the supplementary; a resonance-counting heuristic rather than a derived theorem, and it carries undetermined O(1) coefficients.
  • domain assumption Second-order perturbation theory in the eigenbasis of the largest coupling describes the level spacings inside a bubble.
    Eqs. (45) and (53) of the supplementary assume a small-j expansion; the paper does not check higher-order contributions or the validity of the truncation for the SFD.
  • domain assumption For μ near 2 the model falls into the GOE/GUE/GSE symmetry classes of the Gaussian SYK model (N mod 8).
    Taken from Ref. [26] and used as the RMT baseline for r-ratio and SFF comparisons.

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Cite this review

Pith. "Pith review of L\'evy Sachdev-Ye-Kitaev Model." pith.science (2026). https://pith.science/paper/EEITLFY7

@misc{pith2026250604343,
  author       = {Pith},
  title        = {Pith review of: L\'evy Sachdev-Ye-Kitaev Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EEITLFY7}},
  note         = {Machine review of arXiv:2506.04343}
}
abstract

We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a L\'evy Stable (fat-tailed) distribution. L\'evy random matrices are known to demonstrate non-ergodic behaviour through the emergence of a mobility edge. We study the eigenvalue distribution, focusing on long- and short-range correlations and extreme statistics. This model demonstrates a crossover from chaotic to integrable behaviour (in the spectral correlations) as the distribution becomes increasingly fat-tailed. We investigate this crossover through a hierarchical analysis of the eigenvalue spectrum, based on the multi-fractal hierarchy of the L\'evy Stable distribution. The crossover is explained in terms of a genuine many-body effect, distinct from the transition (controlled by a mobility edge) in the L\'evy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions.

Figures

Figures reproduced from arXiv: 2506.04343 by the authors.

Figure 1
Figure 1. FIG. 1. Interaction graph for 20 Majorana fermions (corre [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (Mean) Nearest neighbor level spacing ratio for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Crossover scale parameter [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (11 more)
Figure 6
Figure 6. Figure 6: FIG. 6. The time [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Scaling of the critical [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of the connected and full spectral form factors (on the log-log scale), with the Heisenberg [PITH_FULL_IMAGE:figures/full_fig_p009_1.png]
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Deviation of the [PITH_FULL_IMAGE:figures/full_fig_p010_2.png]
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The average density of states [PITH_FULL_IMAGE:figures/full_fig_p011_3.png]
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Scaling of the ground state energy with [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Increase of the ratio [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) SFF computed using unfolded spectrum for [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Scaling of the Thouless time [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Short- and long-range correlations for the defect-deformed L´evy SYK ( [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Short- and long-range correlations for the mass-deformed L´evy SYK ( [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

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Works this paper leans on

52 extracted references · 36 canonical work pages

  1. [8]

    Krajewski, M

    T. Krajewski, M. Laudonio, R. Pascalie, and A. Tanasa, Non-gaussian disorder average in the sachdev-ye-kitaev model, Phys. Rev. D99, 126014 (2019)

    work page 2019

  2. [1]

    Sachdev and J

    S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum heisenberg magnet, Phys. Rev. Lett. 70, 3339 (1993)

    1993

  3. [2]

    Kitaev, A simple model of quantum holography

    A. Kitaev, A simple model of quantum holography

    work page

  4. [3]

    Maldacena and D

    J. Maldacena and D. Stanford, Remarks on the sachdev- ye-kitaev model, Phys. Rev. D94, 106002 (2016)

    2016

  5. [4]

    Rossini, G

    D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Quantum advantage in the charging process of sachdev-ye-kitaev batteries, Phys. Rev. Lett.125, 236402 (2020)

    2020

  6. [5]

    W. Fu, D. Gaiotto, J. Maldacena, and S. Sachdev, Super- symmetric sachdev-ye-kitaev models, Phys. Rev. D95, 026009 (2017)

    work page 2017

  7. [6]

    Witten, An syk-like model without disorder, Journal of Physics A: Mathematical and Theoretical52, 474002 (2019)

    E. Witten, An syk-like model without disorder, Journal of Physics A: Mathematical and Theoretical52, 474002 (2019)

    work page 2019

  8. [7]

    S¨ underhauf, L

    C. S¨ underhauf, L. Piroli, X.-L. Qi, N. Schuch, and J. I. Cirac, Quantum chaos in the brownian syk model with large finite n : Otocs and tripartite information, Journal of High Energy Physics2019, 38 (2019)

    work page 2019

Show all 52 references
  1. [9]

    Tezuka, O

    M. Tezuka, O. Oktay, E. Rinaldi, M. Hanada, and F. Nori, Binary-coupling sparse sachdev-ye-kitaev model: An improved model of quantum chaos and holography, Phys. Rev. B107, L081103 (2023)

    2023

  2. [10]

    Hanada, A

    M. Hanada, A. Jevicki, X. Liu, E. Rinaldi, and M. Tezuka, A model of randomly-coupled Pauli spins, JHEP05, 280, arXiv:2309.15349 [hep-th]

    arXiv

  3. [11]

    Andreanov, M

    A. Andreanov, M. Carrega, J. Murugan, J. Olle, D. Rosa, and R. Shir, From dyson models to many-body quantum chaos, Phys. Rev. B111, 035147 (2025)

    2025

  4. [12]

    A. M. Garc ´ ıa-Garc ´ ıa, Y. Jia, D. Rosa, and J. J. M. Verbaarschot, Sparse sachdev-ye-kitaev model, quantum 7 chaos, and gravity duals, Phys. Rev. D103, 106002 (2021)

    2021

  5. [13]

    S. Xu, L. Susskind, Y. Su, and B. Swingle, A sparse model of quantum holography (2020), arXiv:2008.02303 [cond- mat.str-el]

    2020 arXiv

  6. [14]

    C´ aceres, A

    E. C´ aceres, A. Misobuchi, and A. Raz, Spectral form fac- tor in sparse syk models, Journal of High Energy Physics 2022, 236 (2022)

    2022

  7. [15]

    B. V. Gnedenko and A. N. Kolmogorov,Limit dis- tributions for sums of independent random variables (Addison-Wesley., 1954)

    1954

  8. [16]

    J. P. Nolan,Univariate Stable Distributions(Springer Cham, 2020)

    2020

  9. [17]

    Janzen, A

    K. Janzen, A. Engel, and M. M´ ezard, Thermodynamics of the l´ evy spin glass, Phys. Rev. E82, 021127 (2010)

    2010

  10. [18]

    Cizeau and J

    P. Cizeau and J. P. Bouchaud, Theory of l´ evy matrices, Phys. Rev. E50, 1810 (1994)

    1994

  11. [19]

    Biroli and M

    G. Biroli and M. Tarzia, L´ evy-rosenzweig-porter random matrix ensemble, Phys. Rev. B103, 104205 (2021)

    2021

  12. [20]

    Burda, R

    Z. Burda, R. A. Janik, J. Jurkiewicz, M. A. Nowak, G. Papp, and I. Zahed, Free random l´ evy matrices, Phys. Rev. E65, 021106 (2002)

    2002

  13. [21]

    Burda, J

    Z. Burda, J. Jurkiewicz, M. A. Nowak, G. Papp, and I. Zahed, Free random l´ evy and wigner-l´ evy matrices, Phys. Rev. E75, 051126 (2007)

    2007

  14. [22]

    ´Slezak, StableDistributions.jl (2024)

    J. ´Slezak, StableDistributions.jl (2024)

    2024

  15. [23]

    C. Monthus, Localization transition in random l´ evy ma- trices: multifractality of eigenvectors in the localized phase and at criticality, Journal of Statistical Mechan- ics: Theory and Experiment2016, 093304 (2016)

    2016

  16. [24]

    Tarquini, G

    E. Tarquini, G. Biroli, and M. Tarzia, Level statistics and localization transitions of l´ evy matrices, Phys. Rev. Lett. 116, 010601 (2016)

    2016

  17. [25]

    Varga,Gerˇ sgorin and His Circles, Springer Series in Computational Mathematics (Springer Berlin Heidel- berg, 2011)

    R. Varga,Gerˇ sgorin and His Circles, Springer Series in Computational Mathematics (Springer Berlin Heidel- berg, 2011)

    2011

  18. [26]

    A. M. Garc ´ ıa-Garc ´ ıa and J. J. M. Verbaarschot, Spectral and thermodynamic properties of the sachdev-ye-kitaev model, Phys. Rev. D94, 126010 (2016)

    2016

  19. [27]

    Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, Distri- bution of the ratio of consecutive level spacings in random matrix ensembles, Phys. Rev. Lett.110, 084101 (2013)

    2013

  20. [28]

    Oganesyan and D

    V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B75, 155111 (2007)

    2007

  21. [29]

    D. S. Dean and S. N. Majumdar, Large deviations of extreme eigenvalues of random matrices, Phys. Rev. Lett. 97, 160201 (2006)

    2006

  22. [30]

    S. N. Majumdar, Extreme eigenvalues of wishart ma- trices: application to entangled bipartite system, arXiv preprint arXiv:1005.4515 (2010)

    2010 arXiv

  23. [31]

    Auffinger and S

    A. Auffinger and S. Tang, Extreme eigenvalues of sparse, heavy tailed random matrices, Stochastic Processes and their Applications126, 3310 (2016)

    2016

  24. [32]

    Winn, Extreme eigenvalues of random matrices from jacobi ensembles, arXiv preprint arXiv:2302.12082 (2023)

    B. Winn, Extreme eigenvalues of random matrices from jacobi ensembles, arXiv preprint arXiv:2302.12082 (2023)

    2023 arXiv

  25. [33]

    Jevicki, K

    A. Jevicki, K. Suzuki, and J. Yoon, Bi-Local Holography in the SYK Model, JHEP07, 007, arXiv:1603.06246 [hep- th]

    arXiv

  26. [34]

    B¨ acker, F

    A. B¨ acker, F. Steiner, and P. Stifter, Spectral statistics in the quantized cardioid billiard, Phys. Rev. E52, 2463 (1995)

    1995

  27. [35]

    Buijsman, V

    W. Buijsman, V. Cheianov, and V. Gritsev, Sensitivity of the spectral form factor to short-range level statistics, Phys. Rev. E102, 042216 (2020)

    2020

  28. [36]

    Orman, H

    P. Orman, H. Gharibyan, and J. Preskill, Quantum chaos in the sparse SYK model, (2024), arXiv:2403.13884 [hep- th]

    2024 arXiv

  29. [37]

    Haake, Quantum signatures of chaos, inQuantum Co- herence in Mesoscopic Systems(Springer, 1991)

    F. Haake, Quantum signatures of chaos, inQuantum Co- herence in Mesoscopic Systems(Springer, 1991)

    1991

  30. [38]

    M. L. Mehta,Random matrices, 3rd ed., Pure and applied mathematics: v. 142 (Elsevier/Academic Press, Amster- dam, 2004)

    2004

  31. [39]

    Rela˜ no, J

    A. Rela˜ no, J. M. G. G´ omez, R. A. Molina, J. Retamosa, and E. Faleiro, Quantum chaos and 1/fnoise, Phys. Rev. Lett.89, 244102 (2002)

    2002

  32. [40]

    Winer and B

    M. Winer and B. Swingle, Hydrodynamic theory of the connected spectral form factor, Phys. Rev. X12, 021009 (2022)

    2022

  33. [41]

    Cotler, N

    J. Cotler, N. Hunter-Jones, J. Liu, and B. Yoshida, Chaos, Complexity, and Random Matrices, JHEP11, 048, arXiv:1706.05400 [hep-th]

    arXiv

  34. [42]

    J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, Black Holes and Random Matrices, JHEP05, 118, [Erratum: JHEP 09, 002 (2018)], arXiv:1611.04650 [hep-th]

    2018 arXiv

  35. [43]

    Pieper, M

    A. Pieper, M. Kreutzer, A. Alvermann, M. Galgon, H. Fehske, G. Hager, B. Lang, and G. Wellein, High- performance implementation of chebyshev filter diago- nalization for interior eigenvalue computations, Journal of Computational Physics325, 226 (2016)

    2016

  36. [44]

    Rosa, ChebyshevFiltering.jl (2023)

    D. Rosa, ChebyshevFiltering.jl (2023)

    2023

  37. [45]

    ˇSuntajs, J

    J. ˇSuntajs, J. Bonˇ ca, T. Prosen, and L. Vidmar, Quan- tum chaos challenges many-body localization, Phys. Rev. E102, 062144 (2020)

    2020

  38. [46]

    A. S. Matsoukas-Roubeas, M. Beau, L. F. Santos, and A. del Campo, Unitarity breaking in self-averaging spec- tral form factors, Phys. Rev. A108, 062201 (2023)

    2023

  39. [47]

    C. A. Tracy and H. Widom, Level-spacing distributions and the airy kernel, Communications in Mathematical Physics159, 151 (1994)

    1994

  40. [48]

    Nadal and S

    C. Nadal and S. N. Majumdar, A simple derivation of the tracy–widom distribution of the maximal eigenvalue of a gaussian unitary random matrix, Journal of Statis- tical Mechanics: Theory and Experiment2011, P04001 (2011)

    2011

  41. [49]

    Sun and J

    F. Sun and J. Ye, Periodic table of the ordinary and su- persymmetric sachdev-ye-kitaev models, Phys. Rev. Lett. 124, 244101 (2020)

    2020

  42. [50]

    Cipolloni, L

    G. Cipolloni, L. Erd˝ os, and D. Schr¨ oder, Edge universal- ity for non-hermitian random matrices, Probability The- ory and Related Fields179, 1 (2021)

    2021

  43. [51]

    Z. Xiao, R. Shindou, and K. Kawabata, Universal hard- edge statistics of non-hermitian random matrices, Phys. Rev. Res.6, 023303 (2024)

    2024

  44. [52]

    typical value

    A. Kutlin and I. M. Khaymovich, Anatomy of the eigen- states distribution: A quest for a genuine multifractality, SciPost Phys.16, 008 (2024), arXiv:2309.06468 [cond- mat.stat-mech]. 1 Supplemental Material for L´ evy Sachdev-Ye-Kitaev Model DET AILS OF NUMERICAL COMPUT A TION...

    2024 arXiv

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