Quantum critical response at the onset of spin density wave order in two-dimensional metals

TL;DR

This paper investigates the frequency-dependent electron self energy and optical conductivity near a spin density wave quantum critical point in 2D metals, revealing non-Fermi liquid behavior and singular low-frequency conductivity due to hot spot scattering and composite operators.

Contribution

It introduces a detailed analysis of the interplay between hot and cold Fermi surface regions and highlights the role of composite operators like phi^2 in driving non-Fermi liquid behavior across the entire Fermi surface.

Findings

Non-Fermi liquid behavior induced by phi^2 composite operators.

An intermediate frequency regime where cold electrons lose quasiparticles.

Singular low-frequency optical conductivity due to umklapp scattering.

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, \phi, 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 $\phi$ fields: these have important effects also away from the hot spots. The simplest composite operator, \phi^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.