Europhys. Lett.
Volume 67, Number 1, July 2004
Page(s) 84 - 89
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 01 June 2004
Europhys. Lett., 67 (1) , pp. 84-89 (2004)
DOI: 10.1209/epl/i2004-10048-2

Critical level spacing distribution in long-range hopping Hamiltonians

E. Cuevas

Departamento de Física, Universidad de Murcia - E-30071 Murcia, Spain

(Received 22 January 2004; accepted in final form 3 May 2004)

The nearest level spacing distribution $P_\ab{c}(s)$ 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 $P_\ab{c}(s)$ has the asymptotic form $P_\ab{c}(s)\sim\exp[-A_ds^{\alpha}]$ 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.

71.30.+h - Metal-insulator transitions and other electronic transitions.
72.15.Rn - Localization effects (Anderson or weak localization).
71.55.Jv - Disordered structures; amorphous and glassy solids.

© EDP Sciences 2004