Dispersions, weights, and widths of the single-particle spectral function in the normal phase of a Fermi gas

TL;DR

This paper investigates the spectral function of a Fermi gas with pair correlations, revealing how dispersions relate to pseudo-gap and contact energy scales, and contrasting behaviors in attractive versus repulsive interactions.

Contribution

It provides a detailed analysis of spectral function features across wave vectors, identifying key energy scales and differentiating interaction types in the normal phase of a Fermi gas.

Findings

Identification of pseudo-gap energy scale near Fermi wave vector

Distinction between crossing and avoided crossing behaviors

Analogy with local spin waves in magnetic materials

Abstract

The dispersions, weights, and widths of the peaks of the single-particle spectral function in the presence of pair correlations, for a Fermi gas with either attractive or repulsive short-range inter-particle interaction, are determined in the normal phase over a wide range of wave vectors, with a twofold purpose. The first one is to determine how these dispersions identify both an energy scale known as the pseudo-gap near the Fermi wave vector, as well as an additional energy scale related to the contact C at large wave vectors. The second one is to differentiate the behaviors of the repulsive gas from the attractive one in terms of crossing versus avoided crossing of the dispersions near the Fermi wave vector. An analogy will also be drawn between the occurrence of the pseudo-gap physics in a Fermi gas subject to pair fluctuations and the persistence of local spin waves in the normal phase of magnetic materials.