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 order parameter, ϕ, 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 out of products of the primary electron or $\varphi$ fields: these have important effects also away from the hot spots. The simplest composite operator, ϕ^2, leads to non-Fermi liquid behavior on the entire Fermi surface. We also find an intermediate frequency window in which the cold electrons loose 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.

72 pages, 23 figures

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