Spectral properties of supersymmetric Polychronakos spin chain associated with AN−1 root system

By using the exact partition function of su(m|n) Polychronakos spin chain associated with AN−1 root system, we numerically study some statistical properties of the related spectrum. It appears 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.