On the size scaling of the nearest level spacing at criticality

Abstract

It is conjectured that the size scaling of the nearest level spacing in the critical spectral region, $S(N)\propto N^{-λ}$, remains qualitatively the same within phases of extended and critical states. The exponent $λ$ is therefore identical to that for the bare level spacing (at zero disorder). Our calculation of the scaling for the one-dimensional model with diagonal disorder and long-range power-like interaction confirms the conjecture.