Quantum critical behavior near a density-wave instability in an isotropic Fermi liquid

TL;DR

This paper investigates the quantum critical behavior of an isotropic Fermi liquid near a density-wave transition, revealing a crossover in fermionic self-energy and a divergence of effective mass exactly at the critical point.

Contribution

It demonstrates that Landau damping causes a self-generated locality, leading to a divergence of effective mass precisely at the quantum critical point.

Findings

Fermionic self-energy crosses over from momentum-dependent to frequency-dependent near the transition.

Effective mass diverges exactly at the quantum critical point, not before.

Fermi liquid behavior persists up to the critical point.

Abstract

We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector q_c. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from Sigma(k,omega) ~ Sigma(k) to Sigma(k,omega) ~ Sigma(omega), where k and omega are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before, i.e., the Fermi liquid survives up to the critical point.