Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal

TL;DR

This paper investigates how collective excitations with different angular momenta behave near a Pomeranchuk quantum critical point, revealing their stability and spectral evolution across Fermi liquid and non-Fermi liquid regimes.

Contribution

It provides a comprehensive scaling function for the electron polarization bubble at any angular momentum, elucidating the evolution of spectral functions during the Fermi liquid to non-Fermi liquid crossover.

Findings

Collective excitations remain stable across the quantum critical point.

Spectral functions for even and odd $l$ evolve smoothly during the crossover.

The derived scaling function interpolates between Fermi liquid and non-Fermi liquid behaviors.

Abstract

We examine the spectral properties of collective excitations with finite angular momentum $l$ for a system of interacting fermions near a Pomeranchuk quantum critical point, both in the Fermi liquid and non-Fermi liquid regimes. Previous studies found that deep in the Fermi liquid regime, the spectral functions for even and odd $l$ behave differently - the latter is suppressed compared to the former because of kinematic constraints on scattering processes. The main focus of our paper is to understand how the spectral functions for even and odd $l$ evolve as the system enters the non-Fermi liquid regime. We obtain the full scaling function for the electron polarization bubble at arbitrary $l$, which interpolates between the Fermi liquid and non-Fermi liquid regimes. We show that collective excitations for all $l$ remain stable and causal throughout the crossover and right at the quantum critical point.