From Dyson Models to Many-Body Quantum Chaos

TL;DR

This paper investigates the transition to many-body quantum chaos in perturbed SYK models on graphs, highlighting the role of single-particle geometry over interactions, verified through advanced numerical methods.

Contribution

It introduces a novel perspective on many-body quantum chaos by linking it to single-particle properties in graph-based SYK models, emphasizing the geometric features.

Findings

Single-particle geometry dominates the chaos transition.

Numerical methods successfully analyze large Hamiltonians.

The approach offers a new single-particle viewpoint on many-body chaos.

Abstract

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.