The Huang-Yang conjecture for the low-density Fermi gas

TL;DR

This paper proves the Huang-Yang conjecture by establishing a precise asymptotic expansion of the ground state energy for dilute spin-1/2 Fermi gases with short-range repulsive interactions, confirming a 1957 prediction.

Contribution

It provides the first rigorous proof of the Huang-Yang formula for the ground state energy in dilute Fermi gases, completing the asymptotic analysis.

Findings

Validated the universal formula depending only on scattering length

Established matching upper and lower bounds for the energy

Confirmed the conjecture for a broad class of interaction potentials

Abstract

Our work establishes a three-term asymptotic expansion of the ground state energy of a dilute gas of spin $1/2$ fermions with repulsive short-range interactions, validating a formula predicted by Huang and Yang in 1957. The formula is universal in the sense that it holds for a large class of interaction potentials and depends on those only via their scattering length. We have recently proved an upper bound on the ground state energy of the desired form, and the present work completes the program by proving the matching lower bound.