Fluctuation effects at the onset of $\bf 2k_F$ density wave order with two pairs of hot spots in two-dimensional metals

TL;DR

This paper investigates quantum fluctuation effects at the onset of density wave order in two-dimensional metals, revealing non-Fermi liquid behavior and analyzing the stability of the quantum critical point through perturbative and self-consistent methods.

Contribution

It provides a detailed analysis of fluctuation effects at the $2k_F$ density wave transition, including a self-consistent approach that stabilizes the quantum critical point.

Findings

Non-Fermi liquid behavior with linear decay rate

Finite renormalizations of Fermi velocity and curvature

Stability of the quantum critical point with self-energy feedback

Abstract

We analyze quantum fluctuation effects at the onset of charge or spin density wave order in two-dimensional metals with an incommensurate nesting ($2k_F$) wave vector connecting two pairs of hot spots on the Fermi surface. We first compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a perturbation expansion (one loop). Non-Fermi liquid behavior with a linear (in energy) quasi-particle decay rate and a logarithmically vanishing quasi-particle weight is obtained. The momentum dependence of the self-energy entails only finite renormalizations of the Fermi velocity and the Fermi surface curvature at the hot spots. The perturbative one-loop result is not self-consistent and casts doubt on the stability of the $2k_F$ quantum critical point. We construct a self-consistent solution of the one-loop equations with self-energy feedback, where the quantum critical point is stabilized rather than being destroyed by fluctuations, while the non-Fermi liquid behavior as found in the perturbative one-loop calculation is confirmed.