Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system

TL;DR

This paper investigates the spectral properties of the supersymmetric Polychronakos spin chain linked to the A_{N-1} root system, revealing Gaussian energy level densities and a specific spacing distribution law.

Contribution

It provides the first detailed analysis of the spectral statistics of this spin chain model, highlighting its Gaussian level density and unique spacing distribution.

Findings

Energy level density follows a Gaussian distribution

Spacing between energy levels obeys a 'square root of a logarithm' law

Spectral properties are characterized using the exact partition function

Abstract

By using the exact partition function of su(m|n) Polychronakos spin chain associated with A_{N-1} root system, we study some statistical properties of the related spectrum. It is found that the corresponding energy level density satisfies the Gaussian distribution and the cumulative distribution of spacing between consecutive energy levels obeys a certain `square root of a logarithm' law.