Dilute Fermi gas at fourth order in effective field theory

H.‐W. Hammer, R. J. Furnstahl

R. J. Furnstahl, Brian D. Serot

Emanuela L. Giacomelli

Corbinian Wellenhofer, C. Drischler, A. Schwenk

Using effective field theory methods, we calculate for the first time the complete fourth-order term in the Fermi-momentum or kFas 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 |kFas|≲0.5.

Corbinian Wellenhofer, C. Drischler, A. Schwenk

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or ${k}_{\mathrm{F}}{a}_{s}$ expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well converged at this order for $|{k}_{\mathrm{F}}{a}_{s}|\ensuremath{\lesssim}0.5$. Furthermore, we show that Pad\'e-Borel resummations can improve the convergence for $|{k}_{\mathrm{F}}{a}_{s}|\ensuremath{\lesssim}1$. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.

Dmitri V. Efremov, M. S. Mar’enko, M. A. Baranov +1 more

Higher-order perturbation-theory corrections to the superfluid transition temperature in a weakly nonideal Fermi gas with repulsion are determined. This involves calculating the contribution of third-and fourth-order diagrams in terms of the gas parameter ap F to the effective interaction which determines the super-fluid transition temperature and also allowing for effects associated with retardation and renormalization of the polar part of the Green’s function. The expressions obtained provide evidence in support of attraction in the effective interaction in the second, third, and fourth orders of perturbation theory. It is shown that the critical temperature is mainly determined by second-and third-order terms of perturbation theory. Calculations are made of the superfluid transition temperature for a gas comprising neutral Fermi particles in a magnetic field. The limits of validity of the theory are analyzed and the possibility of applying the results to dilute solutions of 3 He in 4 He and neutral-particle Fermi gases in magnetic traps is discussed.