On the eigenvalue distribution of the Sachdev-Ye-Kitaev Model

We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are nonrandom, while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large $N$ , where $N$ is the number of Majorana fermion operators, and also in the limit of large $N$ and $M$ , where $M$ is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite $N$ , we also study the distribution of the eigenvalues of the SYK Lindbladians.We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are nonrandom, while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large $N$, where $N$ is the number of Majorana fermion operators, and also in the limit of large $N$ and $M$, where $M$ is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite $N$, we also study the distribution of the eigenvalues of the SYK Lindbladians.

arXiv:2112.13489Physical review. B./Physical review. BAug 22, 202250 citations

Lévy Sachdev-Ye-Kitaev model

Budhaditya Bhattacharjee, William E. Salazar, Dario Rosa +1 more

We explore the spectral properties of the $4$ -fermion Sachdev-Ye-Kitaev model with interaction sourced from a Lévy Stable (fat-tailed) distribution. Lévy 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 Lévy 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 Lévy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions.We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a Lévy Stable (fat-tailed) distribution. Lévy 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 Lévy 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 Lévy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions.

arXiv:2506.04343Physical review. B./Physical review. BAug 13, 20260 citations

A Numerical Analysis of Thermalization in the Sachdev-Ye-Kitaev Model

Ioanna Kourkoulou

May 1, 20170 citations

Level Statistics of the Sachdev-Ye-Kitaev Model

Yi‐Zhuang You, Andreas W. W. Ludwig, Cenke Xu

Bulletin of the American Physical SocietyMar 13, 20170 citations

Low-rank Sachdev-Ye-Kitaev models

Jaewon Kim, Xiangyu Cao, Ehud Altman

Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the ( $q=4$ ) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix ${J}_{ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. More generic distributions give rise to ``almost Fermi liquids'' with a scaling dimension $\mathrm{\ensuremath{\Delta}}=1/2$, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the ($q=4$) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix ${J}_{ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. More generic distributions give rise to ``almost Fermi liquids'' with a scaling dimension $\mathrm{\ensuremath{\Delta}}=1/2$, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.

arXiv:1910.10173Physical review. B./Physical review. BMar 16, 202032 citations

N

, where

N

is the number of Majorana fermion operators, and also in the limit of large

N

and

M

, where

M

is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite

N

, we also study the distribution of the eigenvalues of the SYK Lindbladians.

We explore the spectral properties of the

4

-fermion Sachdev-Ye-Kitaev model with interaction sourced from a Lévy Stable (fat-tailed) distribution. Lévy 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 Lévy 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 Lévy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions.

Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the (

q=4

) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix

{J}_{ij,kl}

are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. More generic distributions give rise to ``almost Fermi liquids'' with a scaling dimension $\mathrm{\ensuremath{\Delta}}=1/2$, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.