Level repulsion in integrable and almost-integrable quantum spin models

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.

15 pages + 7 figures, REVTEX

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