Fragmented eigenstate thermalization versus robust integrability in long-range models

TL;DR

This paper investigates how long-range couplings affect the stability of integrability and thermalization in many-body quantum systems, revealing conditions for robustness or fragility of integrability.

Contribution

It introduces a symmetry-based framework and characterizes the impact of different perturbations on integrability and chaos in fully connected models.

Findings

Chaos is triggered by extensive two-body perturbations at infinitesimal strength.

Integrability stability depends on whether perturbations are non-extensive, one-body, or two-body.

Eigenstate thermalization is fragmented due to symmetry-defined energy bands.

Abstract

Understanding the stability of integrability in many-body quantum systems is key to controlling dynamics and predicting thermalization. While the breakdown of integrability in short-range interacting systems is well understood, the role of long-range couplings -- ubiquitous and experimentally realizable -- remains unclear. We show that in fully connected models, integrability is either robust or extremely fragile, depending on whether perturbations are non-extensive, extensive one-body, or extensive two-body. In contrast to finite short-range systems, where any of these perturbations can induce chaos at finite strength, in fully connected finite models, chaos is triggered by extensive two-body perturbations and even at infinitesimal strength. Chaos develops within energy bands defined by symmetries, leading to a fragmented realization of the eigenstate thermalization hypothesis and clarifying how microcanonical shells can be constructed in such systems. We also introduce a general symmetry-based framework that explains the stability of integrability.