Critical level spacing distribution in long-range hopping Hamiltonians

Abstract

The nearest level spacing distribution $P_c(s)$ of $d$-dimensional disordered models ($d=1$ and 2) with long-range random hopping amplitudes is investigated numerically at criticality. We focus on both the weak ($b^d \gg 1$) and the strong ($b^d \ll 1$) coupling regime, where the parameter $b^{-d}$ plays the role of the coupling constant of the model. It is found that $P_c(s)$ has the asymptotic form $P_c(s)\sim\exp [-A_ds^α]$ for $s\gg 1$, with the critical exponent $α=2-a_d/b^d$ in the weak coupling limit and $α=1+c_d b^d$ in the case of strong coupling.