Resistivity of a non-Galilean Fermi liquid near Pomeranchuk Quantum Criticality

We analyze the effect of the electron-electron interaction on the resistivity of a metal near a Pomeranchuk quantum critical point (QCP). We show that Umklapp processes are not effective near a QCP, and one must consider the interplay between interaction and disorder. By power counting, the correction to the residual resistivity at low $T$ scales as $AT^{(D+2)/3}$ at QCP ($T^{4/3}$ in 2D). We show, however, that that $A=0$ for a simply connected and convex Fermi surface in 2D due to hidden integrability of the electron motion. We argue that $A >0$ in a two-band ($s-d$) model with light and heavy carriers, and propose this model as an explanation for the observed $T^{(D+2)/3}$ behavior.