Universal corrections to the Fermi-liquid theory

TL;DR

This paper demonstrates that universal non-analytic corrections arising from singularities in bosonic response functions modify Fermi-liquid predictions, resolving recent controversies with exact expressions showing only specific interaction components matter.

Contribution

It provides exact second-order expressions for non-analytic corrections in 2D Fermi liquids, clarifying the role of interaction components and resolving prior debates.

Findings

Identifies universal non-analytic corrections in 2D Fermi liquids.

Derives exact second-order expressions for these corrections.

Shows only U(0) and U(2p_F) interactions influence the corrections.

Abstract

We show that the singularities in the dynamical bosonic response functions of a generic 2D Fermi liquid give rise to universal, non-analytic corrections to the Fermi-liquid theory. These corrections yield a $T^2$ term in the specific heat, $T$ terms in the effective mass and the uniform spin susceptibility $\chi_s (Q=0,T)$, and $|Q|$ term in $\chi_s (Q,T=0)$. The existence of these terms has been the subject of recent controversy, which is resolved in this paper. We present exact expressions for all non-analytic terms to second order in a generic interaction $U(q)$ and show that only U(0) and $U(2p_F)$ matter.