Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion

TL;DR

This paper investigates how the spin susceptibility of a clean Fermi gas with repulsive interactions varies with temperature across different dimensions, revealing non-analytic behaviors and extending existing theoretical frameworks.

Contribution

It generalizes a supersymmetric low energy theory to include magnetic field coupling, deriving new temperature-dependent corrections to spin susceptibility in various dimensions.

Findings

In 2D and 3D, correction scales as T^{d-1} times a squared renormalized backscattering amplitude.

In 1D, correction is proportional to the backscattering amplitude, matching known results.

The method extends the theoretical understanding of spin susceptibility in interacting Fermi gases.

Abstract

Spin susceptibility of a clean Fermi gas with repulsion in any dimension is considered using a supersymmetric low energy theory of interacting spin excitations and renormalization scheme recently proposed by Aleiner and Efetov [cond-mat/0602309]. We generalize this method to include the coupling to the magnetic field. As a result, we obtain for the correction $\delta \chi $ to the Pauli susceptibility a non-analytic temperature dependence of the form $ T^{d-1}\gamma_{b}^{2}(T)$ in dimensions $d=2,3,$ where $\gamma_{b}(T)$ is an effective $d$-dependent logarithmically renormalized backscattering amplitude. In one dimension, $\delta \chi $ is proportional to $\gamma_{b}(T)$, and we reproduce a well known result obtained long ago by a direct calculation.