# Dilute Fermi gas at fourth order in effective field theory

## TL;DR

This paper computes the complete fourth-order term in the Fermi-momentum expansion for a dilute Fermi gas's ground-state energy using effective field theory, and compares its convergence with quantum Monte-Carlo results.

## Contribution

It provides the first calculation of the fourth-order term in the Fermi-momentum expansion for dilute Fermi gases using effective field theory.

## Key findings

- The expansion converges well for |k_F a_s| ≤ 0.5.
- Comparison with quantum Monte-Carlo results confirms the convergence.
- First complete fourth-order calculation in this context.

## Abstract

Using effective field theory methods, we calculate for the first time the complete fourth-order term in the Fermi-momentum or $k_{\rm F} a_s$ expansion for the ground-state energy of a dilute Fermi gas. The convergence behavior of the expansion is examined for the case of spin one-half fermions and compared against quantum Monte-Carlo results, showing that the Fermi-momentum expansion is well-converged at this order for $| k_{\rm F} a_s | \lesssim 0.5$.