Enhancement of the spin susceptibility in disordered interacting electrons and the metal-insulator transition

The response of a disordered interacting electron gas to a time and spatially varying magnetic field is discussed. Local spin conservation leads to a generalized Ward identity, which together with global spin conservation implies that the dynamic magnetic susceptibility (q,) must obey a simple diffusive form. The same identity, when combined with the general perturbative structure of (q,), also relates the renormalization of static susceptibility st and the spin diffusion constant Ds to the renormalization of the charge diffusion constant and the Fermi-liquid interaction amplitudes. These relations are shown to be consistent with perturbations to first order in t {=1/[(2)2N0D]} but only after nontrivial cancellations. Thus the Ward identity allows both easy derivation of (q,) from the renormalized theory and a consistency check on the scaling equations. By using the renormalization-group equations for these parameters, it is shown that there is strong enhancement of st and decrease in Ds with lowering temperature. The significance of this with respect to the metal-insulator transition is discussed. © 1986 The American Physical Society.