Entanglement production in the Sachdev-Ye-Kitaev Model and its variants

TL;DR

This paper investigates entanglement growth in variants of the Sachdev-Ye-Kitaev (SYK) model, revealing how entanglement dynamics reflect different degrees of quantum chaos and how they evolve with system size.

Contribution

It demonstrates that entanglement production rates vary across SYK variants and serve as a sensitive measure of quantum chaos beyond traditional metrics.

Findings

All variants show initial linear entanglement growth.

Late-time entanglement saturates to a universal RMT-consistent value.

Entanglement growth rates differ and depend on system size.

Abstract

Understanding how quantum chaotic systems generate entanglement can provide insight into their microscopic chaotic dynamics and can help distinguish between different classes of chaotic behavior. Using von Neumann entanglement entropy, we study a nonentangled state evolved under three variants of the Sachdev-Ye-Kitaev (SYK) model with a finite number of Majorana fermions $N$. All the variants exhibit linear entanglement growth at early times, which at late times saturates to a universal value consistent with random matrix theory (RMT), but their growth rates differ. We interpret this as a large-$N$ effect, arising from the enhanced non-locality of fermionic operators in SYK and binary SYK, absent in spin operators of the spin-SYK model. Numerically, we find that these differences emerge gradually with increasing $N$. Although all variants are quantum chaotic, their entanglement dynamics reflect varying degrees of chaos and indicate that the entanglement production rate serves as a fine-grained probe of chaos beyond conventional measures. To probe its effect on thermalization properties of these models, we study the two-point autocorrelation function, finding no differences between the SYK variants, but deviations from RMT predictions for $N \geq 24$, particularly near the crossover from exponential decay to saturation regime.