We consider a model of N species of electrons in a random potential interacting via a short-range repulsive interaction. We study the N= limit and the 1N expansion to the leading order in 1N. After renormalizing the theory, we find that there are three coupling constants in this problem: (i) a coupling constant with the dimensions of the resistivity, (ii) the coupling for electron-electron scattering, and (iii) the coupling strength between diffusive modes and density fluctuations. The renormalization-group equations are presented. In 2+μ dimensions the Anderson fixed point of the noninteracting theory is shown to belong to a line of unstable fixed points. A new ("interacting") fixed point is found. At the transition we find that, to leading order in 1N, (a) the exponent of the localization length is the same as in the noninteracting theory, (b) the dc conductivity vanishes at the mobility edge with an exponent s=217, (c) the density of states at the Fermi surface vanishes at the mobility edge with an exponent =217, (d) the mean free time at the Fermi surface vanishes at the mobility edge with an exponent =717, (e) the Fermi velocity diverges at the mobility edge with an exponent =517, and (f) the diffusive modes acquire wave-function renormalization and the anomalous dimension is (to leading order) equal to μ34.
ASJC Scopus subject areas
- Condensed Matter Physics