Quantum Critical Response at the Onset of Spin Density Wave Order in Two-dimensional Metals

Abstract

We study the frequency dependence of the electron self-energy and the optical conductivity in a recently developed field theory of the spin-density-wave quantum phase transition in two-dimensional metals. We focus on the interplay between the Fermi surface “hot spots” and the remainder of the “cold” Fermi surface. Scattering of electrons off the fluctuations of the spin-density-wave order parameter, \(\varphi\), is strongest at the hot spots; we compute the conductivity due to this scattering in a rainbow approximation. We point out the importance of composite operators, built of products of the primary electron or \(\varphi\) fields: These have important effects also away from the hot spots. The simplest composite operator, \(\varphi^2\), leads to deviations from Landau Fermi-liquid behavior on the entire Fermi surface. We also find an intermediate frequency window in which the cold electrons lose their quasiparticle form due to effectively one-dimensional scattering processes. The latter processes are part of umklapp scattering, which leads to singular contributions to the optical conductivity at the lowest frequencies at zero temperature.