Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.30333

Onset of random-matrix statistics in the Yukawa-Sachdev-Ye-Kitaev model: Spectral correlations and Krylov complexity

Sizheng Cao·Hyun-Sik Jeong·Yi-Li Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Yukawa-Sachdev-Ye-Kitaev (YSYK) model, a solvable model of non-Fermi liquids with a proposed cavity-QED realization, couples $N$ complex fermions to $M$ bosons of frequency $ω_0$ through random Yukawa couplings of strength $g$, and its dynamics depends only on $R\equivω_0/g^{2/3}$. For $R\ll1$ the bosons are slow and act as a static random background in which the fermions are free, while for $R\gg1$ they are only virtually excited and generate a random four-fermion interaction of rank $M$, which is generically chaotic for $M\geq2$. Using exact diagonalization at infinite temperature, we follow the emergence of random-matrix statistics between these limits with unfolded spectral statistics and the Krylov complexity of the thermofield-double state. For complex couplings the level-spacing distribution evolves from Poisson to Gaussian-unitary-ensemble (GUE) statistics, the spectral form factor develops a correlation hole and a ramp, and the Krylov complexity evaluated on the unfolded spectrum develops a peak above its late-time plateau whose height reaches the GUE value. All diagnostics locate the onset around $R\approx0.3$, and adding boson modes moves it to smaller $R$. This delineates the parameter regime in which a cavity-QED realization would display random-matrix spectral correlations. On the other hand, real couplings give the same crossover towards Gaussian-orthogonal-ensemble (GOE) statistics, and along an interpolation between the two the peak height follows the mean gap ratio, so the peak identifies the symmetry class as well as the onset of chaos. Without unfolding the peak stays about 20$\%$ below its random-matrix value in both classes, which we trace to the non-semicircular density of states, and at larger $R$ the boson-number bands slow down the spreading of the state in Krylov space.

Explore related subjects

nlin.CDcond-mat.str-elhep-thquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sizheng Cao, Hyun-Sik Jeong, Yi-Li Wang. 2026-09-24. Onset of random-matrix statistics in the Yukawa-Sachdev-Ye-Kitaev model: Spectral correlations and Krylov complexity. https://arxiv.org/abs/2609.30333

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Geodesic vortex detection on curved surfaces: Analyzing the 2002 austral stratospheric polar vortex warming event

Geodesic vortex detection is a tool in nonlinear dynamical systems to objectively identify transient vortices with flow-invariant boundaries that defy the typical deformation found in 2-d turbulence. Initially formulated for flows on the Euclidean plane with Cartesian coordinates, we have extended this technique to flows on 2-d Riemannian manifolds with arbitrary coordinates. This extension required the further formulation of the concept of objectivity on manifolds. Moreover, a recently proposed birth-and-death vortex framing algorithm, based on geodesic detection, has been adapted to address the limited temporal validity of 2-d motion in otherwise 3-d flows, like those found in the Earth's stratosphere. With these adaptations, we focused on the Lagrangian, i.e., kinematic, aspects of the austral stratospheric polar vortex during the exceptional sudden warming event of 2002, which resulted in the vortex splitting. This study involved applying geodesic vortex detection to isentropic winds from reanalysis data. We provide a detailed analysis of the vortex's life cycle, covering its birth, the splitting process, and its eventual death. In addition, we offer new kinematic insights into ozone depletion within the vortex.

nlin.CD↗
arXiv2026

Regularity and reentry basins of low Earth orbits in the $J_{2}$-solar radiation pressure problem

We numerically investigate the long-term dynamical structure of low Earth orbits (LEOs) using the Smaller Alignment Index (SALI), a fast numerical indicator of chaos, within a closed-form averaged model that incorporates the effects of solar radiation pressure and Earth's oblateness. Our analysis reveals that the area-to-mass ratio is a key parameter governing the onset and extent of chaotic behavior in LEOs. We map the system's chaotic regions, study the behavior of reentry trajectories and characterize their temporal laws over a timescale constrained by the $25$-year mitigation guideline. Within this physically relevant timescale, we show that most of the reentry trajectories exhibit regular motion. Reentry basins, constructed according to different mitigation guidelines up to $25$ years, display fractal-like structures for less-stringent guidelines. The degree of this fractality is quantitatively assessed using the uncertainty exponent method. In most cases, for large area-to-mass ratios, reentry occurs on relatively short timescales (a few years) - short enough that no fractal behavior is observed in the basin boundaries. This numerical dynamical study offers insights into the development of dynamically informed deorbiting strategies.

nlin.CD↗
arXiv2026

Attractor reconstruction in attracting subspaces: Slow-spectrum preshaping for reservoir computing under partial observation

Data-driven reproduction of chaotic dynamics under partial observation remains a challenge despite its practical importance. Reservoir computing (RC) and other data-driven approaches often succeed in short-term prediction but are sensitive to hyperparameters and frequently fail to reproduce the long-term statistical properties of the system. As recently shown, a major cause of this failure is spurious slow modes induced by training, which render the reconstructed invariant set transversally unstable in the representation space. To address this, a design principle called Attractor Reconstruction in Attracting Submanifolds (ARAS) was proposed, which requires the reconstruction to lie in a low-dimensional, transversally attracting submanifold. Under full observation, ARAS was realized by an input-layer design that limits the number of slow modes perturbed during training and anchors the remaining modes to stay fast, thereby suppressing spurious slow modes. However, under partial observation, this design alone fails because the submanifold designed to be attracting cannot retain the observation history needed to unfold the observed data into a faithful reconstruction. In this study, we propose slow-spectrum preshaping, which introduces a slow spectrum into the reservoir prior to feeding input data. The induced slow modes then retain a memory of past observations within the submanifold, while the input-layer design makes the submanifold transversally attracting, so that ARAS is realized under partial observation. Through numerical experiments on various chaotic systems, we show that our approach enables reliable short-term prediction and long-term reproduction of chaos over a wide range of hyperparameters without a posteriori tuning.

nlin.CD↗