Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities

TL;DR

This paper introduces a quasi-Gaussian approximation to analyze strongly correlated imbalanced fermions, revealing universal scaling laws and critical polarization ratios for phase separation in three-dimensional unitary fermions.

Contribution

It develops a novel quasi-Gaussian scheme capturing non-Gaussian correlations via geometric mean susceptibilities, applicable to strongly correlated fermionic systems beyond mean-field theory.

Findings

Critical polarization ratio for phase separation: approximately 0.34.

Universal nonlinear scaling relates chemical potentials and Fermi energies.

Ground state energy density ratio: 4/9.

Abstract

A quasi-Gaussian approximation scheme is formulated to study the strongly correlated imbalanced fermions thermodynamics, where the mean-field theory is not applicable. The non-Gaussian correlation effects are understood to be captured by the statistical geometric mean of the individual susceptibilities. In the three-dimensional unitary fermions ground state, an {\em universal} non-linear scaling transformation relates the physical chemical potentials with the individual Fermi kinetic energies. For the partial polarization phase separation to full polarization, the calculated critical polarization ratio is $P_C={[1-(1-\xi)^{6/5}]}/{[1+(1-\xi)^{6/5}]}\doteq 0.34$. The $\xi=4/9$ defines the ratio of the symmetric ground state energy density to that of the ideal fermion gas.