On the level density of spin chains of Haldane--Shastry type

TL;DR

This paper proves that the level density of su(m) Haldane-Shastry spin chains converges to a Gaussian distribution as the number of spins increases, using spectral and asymptotic analysis.

Contribution

It provides a rigorous proof of the Gaussian level density for all su(m) Haldane-Shastry spin chains of type A_{N-1}, extending previous heuristic results.

Findings

Level density approaches Gaussian distribution as N increases

Spectrum described via motifs and dispersion relation asymptotics

Rigorous mathematical proof provided

Abstract

We provide a rigorous proof of the fact that the level density of all su(m) spin chains of Haldane-Shastry type associated with the A_{N-1} root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our approach is based on the study of the large N limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the dispersion relation.