Spread of entanglement in a Sachdev-Ye-Kitaev chain

TL;DR

This paper investigates how entanglement spreads in a chaotic SYK chain, revealing that the system quickly reaches a prethermal state rather than full thermalization, with implications for quantum chaos and holography.

Contribution

It demonstrates that the SYK chain's R extquoteright{}enyi entropy saturates below expected levels, indicating prethermalization despite maximal chaos, a novel insight into entanglement dynamics.

Findings

R extquoteright{}enyi entropy saturates at smaller values for n>1

SYK chain does not rapidly thermalize, instead reaches a prethermal state

Results connect entanglement spread to holographic and chaotic behavior

Abstract

We study the spread of R\'enyi entropy between two halves of a Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield double (TFD) state. The SYK chain model is a model of chaotic many-body systems, which describes a one-dimensional lattice of Majorana fermions, with spatially local random quartic interaction. We find that for integer R\'enyi index $n>1$, the R\'enyi entanglement entropy saturates at a parametrically smaller value than expected. This implies that the TFD state of the SYK chain does not rapidly thermalize, despite being maximally chaotic: instead, it rapidly approaches a prethermal state. We compare our results to the signatures of thermalization observed in other quenches in the SYK model, and to intuition from nearly-$\mathrm{AdS}_2$ gravity.