Two-level correlation function of critical random-matrix ensembles

Abstract

The two-level correlation function $R_{d,\beta }(s)$ of $d$-dimensional disordered models ($d=1$, 2, and 3) with long-range random-hopping amplitudes is investigated numerically at criticality. We focus on models with orthogonal ($\beta =1$) or unitary ($\beta =2$) symmetry in 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 $R_{d,\beta }(s)$ is of the form $R_{d,\beta }(s)=1+\delta (s)-F_{\beta }(s^{\beta }/b^{d\beta })$, where $F_1(x)=\text{erfc}(a_{d,\beta }x)$ and $F_2(x)=\exp (-a_{d,\beta }{x}^2)$, with $a_{d,\beta }$ being a numerical coefficient depending on the dimensionality and the universality class. Finally, the level number variance and the spectral compressibility are also considerded.

RevTex4, 7 two-column pages, 6 .eps figures, 1 table. A new section devoted to the spectral compressibility added. To be published in Phys. Rev. B

References in corpus (1)

• Critical properties in long-range hopping Hamiltonians