Quantum criticality at the metal-insulator transition - art. no. 075105

We introduce an alternative method to analyze the many-body problem with di sorder. The method is an extension of the real space renormalization group based on the operator product expansion. We consider the problem in the pre sence of interactions, a large elastic mean free path, and finite temperatu res. As a result scaling is stopped either by temperature or the length sca le set by the diverging many-body length scale (superconductivity). Due to disorder a superconducting instability might take place at T-SC --> 0, givi ng rise to a metallic phase or T>T-SC. For repulsive interactions at T --> 0 we flow towards the localized phase, which is analyzed within the diffusi ve Finkelstein theory. For strong repulsive backward interactions and nonsp herical Fermi surfaces characterized by \d ln N(b)/ln b\much less than 1 on e finds a fixed point (D*, Gamma (2)*) in the plane (D, Gamma ((Delta))(2)) . [D proportional to (K (F)iota)(-1) is the disorder coupling constant, Gam ma ((Delta))(2) is the particle-hole triplet interaction, b is the length s cale, and N(b) is the number of channels.] For weak disorder, D < D*, one o btains a metallic behavior with the resistance <rho>(D, Gamma ((s))(2), T) = rho (D, Gamma ((s))(2), T) similar or equal to rho *f ((D - D*/D* (1/T-z nu1) [rho* = rho (D*, Gamma (2)*, 1), z = 1, and nu (1) > 2], and large fer romagnetic fluctuations caused by the stable fixed point Gamma (2)*.