Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model

TL;DR

This paper investigates how the spectral properties of a finite-range SYK model change with interaction range, revealing a transition from chaotic to localized behavior akin to many-body localization phenomena.

Contribution

It demonstrates that reducing the two-body interaction range induces a transition to many-body localization, connecting SYK models to localization physics and potential gravity duals.

Findings

Spectral correlations remain chaotic with varying one-body range.

Reducing two-body interaction range causes a transition to Poisson statistics.

Near the transition, spectral features resemble those of Anderson and many-body localization transitions.

Abstract

We study the level statistics of a generalized Sachdev-Ye-Kitaev (SYK) model with two-body and one-body random interactions of finite range by exact diagonalization. Tuning the range of the one-body term, while keeping the two-body interaction sufficiently long-ranged, does not alter substantially the spectral correlations, which are still given by the random matrix prediction typical of a quantum chaotic system. However a transition to an insulating state, characterized by Poisson statistics, is observed by reducing the range of the two-body interaction. Close to the many-body metal-insulator transition, we show that spectral correlations share all features previously found in systems at the Anderson transition and in the proximity of the many-body localization transition. Our results suggest the potential relevance of SYK models in the context of many-body localization and also offer a starting point for the exploration of a gravity-dual of this phenomenon.