Determination of Landau Fermi-liquid parameters of strongly interacting fermions by means of a nonlinear scaling transformation

TL;DR

This paper develops a nonlinear scaling transformation method to determine Landau Fermi-liquid parameters in strongly interacting fermions, providing analytical expressions and universal constants for unitary Fermi gases.

Contribution

It introduces a medium-scaling effective action and auxiliary variables to analytically derive Fermi-liquid parameters for strongly interacting fermions.

Findings

Derived expressions for Fermi-liquid parameters $F_0^s$ and $F_1^s$

Obtained a universal effective mass ratio $m^*/m=10/9$ at unitarity

Performed low-temperature expansions for thermodynamic quantities

Abstract

A nonlinear transformation approach is formulated for the correlated fermions' thermodynamics through a medium-scaling effective action. An auxiliary implicit variable-effective chemical potential is introduced to characterize the non-Gaussian fluctuations physics. By incorporating the nonlocal correlation effects, the achieved grand partition function is made of coupled highly nonlinear parametric equations. Analytically, the low temperature expansions for the strongly interacting unitary Fermi gas are performed for the adiabatic compressibility-sound speed and specific heat with the Sommerfeld lemma. The expressions for the Landau Fermi-Liquid parameters $F_0^s$ and $F_1^s$ of the strongly interacting fermion system are obtained. As a universal constant, the effective fermion mass ratio is $m^*/m={10/9}$ at unitarity.