The Mott Anderson metal insulator transition in n orbital models

The interplay of Coulomb interactions and disorder is formulated on the basis of local gauge invariant models withn orbitals per site. Universality classes of correlation-influenced metal insulator transitions are examined from the conducting region of an approximately semi-elliptical band. The microscopic 1/n expansion is brought into direct correspondence with the 1/(k _F ?) expansion of Altshuler et al. Based on1. the assumption that theO(1/n)-expansion can be exponentiated and2. on the renormalization group β-function for finite length scaling, critical exponents are derived in leading order ofd-2 (d is dimensionality). The density of states-at-E _F as the order parameter vanishes at the critical pointE _c like \(\left| {E_F - E_c } \right|^{\beta _{MA} } \) with \(\beta _{MA} = \frac{1}{{4(d - 2)}}\) for the interacting real matrix (orthogonal) ensemble and \(\beta _{MA} = \frac{1}{{2(d - 2)}}\) for the unitary ensemble. If the bare Coulomb interactionU _b (q)∝q ^1-d is replaced by a general long range interactionV _b (q)∝q ^?x withx>0 ford=2, β_MA depends on the “interaction range exponent”x like β_MA(x) = xβ_MA(1). Also in leading order ofd?2, the conductivity exponent ist=1 for both models with or without time reversal invariance respectively. This implies a correlation-induced crossover fromt=1/2 for unitary Anderson localization (broken time reversal invariance) tot=1 at the Mott Anderson transition.