Non-analytic corrections to the Fermi-liquid behavior

TL;DR

This paper revisits non-analytic corrections to Fermi-liquid behavior, clarifying their origins, parameterization, and specific forms in different dimensions, with implications for understanding low-temperature properties of Fermi liquids.

Contribution

It provides a comprehensive analysis of non-analytic corrections originating from universal singularities, parameterized by two key interaction constants, and clarifies their temperature and momentum dependencies in 2D and 3D systems.

Findings

Non-analytic corrections depend on interaction at q=0 and q=2k_F.

In 3D, spin susceptibility non-analyticity is clarified.

In 2D, explicit forms for specific heat and spin susceptibilities are derived.

Abstract

The issue of non-analytic corrections to the Fermi-liquid behavior is revisited. Previous studies have indicated that the corrections to the Fermi-liquid forms of the specific heat and the static spin susceptibility scale as $T^{D}$ and $T^{D-1}$, respectively (with extra logarithms for $D=1,3$). In addition, the non-uniform spin susceptibility is expected to depend on the bosonic momentum $Q$ in a non-analytic way, i.e., as $Q^{D-1}$ (again with extra logarithms for $D=1,3$). It is shown that these non-analytic corrections originate from the universal singularities in the dynamical bosonic response functions of a generic Fermi liquid. In contrast to the leading, Fermi-liquid forms which depend on the interaction averaged over the Fermi surface, the non-analytic corrections are parameterized by only two coupling constants, which are the components of the interaction potential at momentum transfers $q=0$ and $q=2k_F$. For 3D systems, a recent result of Belitz, Kirkpatrick and Vojta for the spin susceptibility is reproduced and the issue why a non-analytic momentum dependence of the non-uniform spin susceptibility ($Q^{2}\ln |Q|$) is \emph{not}paralleled by a non-analyticity in the $T-$ dependence ($T^2$) is clarified. For the case of a 2D system with a finite-range interaction, explicit forms of the corrections to the specific heat ($\propto T^2$), uniform ($\propto T$) and non-uniform ($\propto |Q|$) spin susceptibilities are obtained. It is shown that previous calculations of the temperature dependences of these quantities in 2D were incomplete. Some of the results and conclusions of this paper have recently been announced in a short communication [A. V. Chubukov and D. L. Maslov, cond-mat/0304381].