Level repulsion in integrable and almost-integrable quantum spin models

TL;DR

This paper investigates how the energy level spacing distribution in quantum spin chains transitions from integrable to non-integrable systems, revealing the influence of coupling on spectral statistics.

Contribution

It provides a numerical analysis of level spacing distributions across different spin models, highlighting the transition from Poisson to GOE statistics as systems become non-integrable.

Findings

Level spacing in integrable models follows Poisson distribution.

Non-integrable models exhibit GOE distribution.

Transition between distributions depends on coupling strength.

Abstract

The repartition of the separation between energy levels of various isotropic S=1/2 antiferromagnetic chains is studied numerically with the aim of investigating the transition from integrable to non-integrable systems. We begin by displaying the level separation distribution of the integrable Bethe chain. Then two non-integrable systems, two coupled chains and a next-nearest-neighbor coupled chain, are studied as a function of the coupling. We examine how the level spacing evolves from the Poisson distribution to the GOE distribution. Finally we consider the Haldane-Shastry $1/r^{2}$ model. A number of conclusions regarding the behaviour and relevance of the level spacing distribution in these spin systems is drawn.