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 $P_c(s)\sim \exp [-A_d{s}^{\alpha }]$ for $s\gg 1$, with the critical exponent $\alpha =2-a_d/b^d$ in the weak coupling limit and $\alpha =1+c_d{b}^d$ in the case of strong coupling.

EPL style, 7 pages, 4 .eps figures, to be published in Europhys. Lett

References in corpus (2)

• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Multifractality of Hamiltonians with power-law transfer terms

Cited by in corpus (1)

• Two-level correlation function of critical random-matrix ensembles