LEVEL-SPACING FUNCTION P(S) AT THE MOBILITY EDGE

We present Lanczos numerical scaling results for the nearest-level-spacing distribution function P(S) favoring a recently proposed random-matrix theory (RMT), which extends the usual RMT appropriate for disordered metals to the Anderson metal-insulator transition. In the three-dimensional (d = 3) tight-binding random-matrix ensemble at the mobility edge we obtain a reasonable overall P(S) fit of the form P(S) = BSe(-Asalpha), where A and B are constants and alpha almost-equal-to 1.31, close to the theoretical value of 2 - 2/d. We study in more detail the tail of this distribution which is compatible with a lower value of alpha. These results are also shown to hold for the critical number variance [[deltaN(E)]2] which obeys the asymptotic law [[deltaN(E)]2] is-proportional-to [N(E)]2-alpha.