Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model

By Antonio M. Garc'ia-Garc'ia, J. Verbaarschot. 2016

340 citations recorded by the source corpus.

We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant of the $k$-body embedded random ensembles studied for several decades in the context of nuclear physics and quantum chaos. We show analytically that the fourth- and sixth-order energy cumulants vanish in the limit of a large number of particles $N\ensuremath{\rightarrow}\ensuremath{\infty}$, which is consistent with a Gaussian spectral density. However, for finite $N$, the tail of the average spectral density is well approximated by a semicircle law. The specific heat coefficient, determined numerically from the low-temperature behavior of the partition function, is consistent with the value obtained by previous analytical calculations. For energy scales of the order of the mean level spacing we show that level statistics are well described by random matrix theory. Due to the underlying Clifford algebra of the model, the universality class of the spectral correlations depends on $N$. For larger energy separations we identify an energy scale that grows with $N$, reminiscent of the Thouless energy in mesoscopic physics, where deviations from random matrix theory are observed. Our results are a further confirmation that the Sachdev-Ye-Kitaev model is quantum chaotic for all time scales. According to recent claims in the literature, this is an expected feature in field theories with a gravity dual.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba6a647b79fbcd13fb6daff2597e4d6076cd79d5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Onset of random matrix behavior in scrambling systems (2018, methodology): “This was first applied to the SYK model in [7].”
A semiclassical ramp in SYK and in gravity (2018, background): “etween eigenvalues (see [28], or [29] for a recent overview). The plateau arises from a modication of this power-law form once we consider very small energy dierences that are 4For related work see [23, 24]. 5For related work on correlation functions see [26, 27]. 3 10 0 10 1 10 2 10 3 10 4 10 5 10 ”
Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models (2017, background): “The corresponding expression in the SYK model is [5, 18, 19]”
JT gravity as a matrix integral (2019, background): “One of the motivations for this work was to understand the origin of random matrix statistics in the SYK model [62, 63, 20, 13] from the gravitational perspective.”
Black holes and random matrices (2016, neutral): “(After we had finished our numerical analysis the paper [33] appeared.”
Chaos, complexity, and random matrices (2017, background): “Furthermore, the spectral density of SYK and its relation to random matrices has also been discussed in [24].”