Wilson ratio of Fermi gases in one dimension

TL;DR

This paper calculates the Wilson ratio for one-dimensional Fermi gases with spin imbalance, revealing universal features of quantum liquids and anomalous behavior at critical points despite the breakdown of quasiparticle descriptions.

Contribution

It provides a theoretical calculation of the Wilson ratio in 1D Fermi gases, linking it to density stiffness and sound velocity, and highlights its universality across dimensions.

Findings

Wilson ratio determined by density stiffness and sound velocity

Anomalous enhancement at critical points due to density of states changes

Specific heat remains linear, susceptibility temperature-independent

Abstract

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.