Dilute Fermi gas at fourth order in effective field theory

Abstract

Using effective field theory methods, we calculate for the first time the complete fourth-order term in the Fermi-momentum or $k_{\mathrm{F}}{a}_s$ 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 $|k_{\mathrm{F}}{a}_s|\lesssim 0.5$.

Comments: 6 pages, 2 figures; v2: minor improvements in text, references updated, matches published version