ENERGY-LEVEL STATISTICS IN DISORDERED METALS WITH AN ANDERSON TRANSITION

We present numerical scaling results for the energy level statistics i n orthogonal and symplectic tight-binding Hamiltonian random matrix en sembles defined on disordered two and three-dimensional electronic sys tems with and without spinorbit coupling (SOC), respectively. In the m etallic phase for weak disorder the nearest level spacing distribution function P(S), the number variance [(delta N)(2)], and the two-point correlation function K-2(epsilon) are shown to be described by the Gau ssian random matrix theories. In the insulating phase, for strong diso rder, the correlations vanish for large scales and the ordinary Poisso n statistics is asymptotically recovered, which is consistent with loc alization of the corresponding eigenstates. At the Anderson metal-insu lator transition we obtain new universal scale-invariant distribution functions describing the critical spectral density fluctuations.