Many-body spectral transitions through the lens of variable-range SYK2 model

TL;DR

This paper explores how distance-dependent interactions in a quadratic SYK model affect spectral properties and quantum chaos, revealing transitions from chaotic to localized regimes through spectral form factor analysis.

Contribution

It introduces a variable-range SYK2 model and analyzes its spectral transitions, highlighting the robustness and breakdown of spectral features with changing interaction ranges.

Findings

Spectral form factor remains robust under slight interaction range reductions.

Further suppression of interactions causes spectral regime changes and secondary plateau emergence.

Results connect single-particle criticality with many-body spectral transitions.

Abstract

The Sachdev-Ye-Kitaev (SYK) model is a cornerstone in the study of quantum chaos and holographic quantum matter. Real-world implementations, however, deviate from the idealized all-to-all connectivity, raising questions about the robustness of its chaotic properties. In this work, we investigate a quadratic SYK model with distance-dependent interactions governed by a power-law decay. By analytically and numerically studying the spectral form factor (SFF), we uncover how the single particle transitions manifest in the many-body system. While the SFF demonstrates robustness under slightly reduced interaction ranges, further suppression leads to a breakdown of perturbation theory and new spectral regimes, marked by a higher dip and the emergence of a secondary plateau. Our results highlight the interplay between single-particle criticality and many-body dynamics, offering new insights into the quantum chaos-to-localization transition and its reflection in spectral statistics.