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

Abstract

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 χ(q,Ω) must obey a simple diffusive form. The same identity, when combined with the general perturbative structure of χ(q,Ω), also relates the renormalization of static susceptibility ${\chi }^{\mathrm{st}}$ and the spin diffusion constant $D_s$ 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/[(2π${)}^2$ $N_0$D]} but only after nontrivial cancellations. Thus the Ward identity allows both easy derivation of χ(q,Ω) 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 ${\chi }^{\mathrm{st}}$ and decrease in $D_s$ with lowering temperature. The significance of this with respect to the metal-insulator transition is discussed.