Non Fermi liquid behavior at flat hot spots from quantum critical fluctuations at the onset of charge- or spin-density wave order

TL;DR

This paper investigates non-Fermi liquid behavior at hot spots on the Fermi surface caused by quantum critical fluctuations at the onset of charge or spin density wave order, revealing universal anomalous dimensions and vanishing quasiparticle weight.

Contribution

It provides a detailed one-loop analysis of susceptibility and self-energy at hot spots with vanishing curvature, uncovering universal power-law signatures of non-Fermi liquid behavior.

Findings

Susceptibility peaks sharply at the ordering wave vector Q.

Self-energy shows linear frequency dependence and logarithmic divergences.

Quasiparticle weight vanishes at hot spots, indicating non-Fermi liquid state.

Abstract

We analyze quantum fluctuation effects at the onset of charge or spin density wave order with a $2k_F$ wave vector $\mathbf{Q}$ in two-dimensional metals -- for the special case where $\mathbf{Q}$ connects a pair of hot spots situated at high symmetry points of the Fermi surface with a vanishing Fermi surface curvature. We compute the order parameter susceptibility and the fermion self-energy in one-loop approximation. The susceptibility has a pronounced peak at $\mathbf{Q}$, and the self-energy displays non-Fermi liquid behavior at the hot spots, with a linear frequency dependence of its imaginary part. The real part of the one-loop self-energy exhibits logarithmic divergences with universal prefactors as a function of both frequency and momentum, which may be interpreted as perturbative signatures of power laws with universal anomalous dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing quasiparticle weight at the hot spots, and a renormalized dispersion relation with anomalous algebraic momentum dependencies near the hot spots.