Effective field theory for dilute Fermi systems

R. J. Furnstahl, Brian D. Serot

C. Drischler, Corbinian Wellenhofer, K. Hebeler +1 more

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.

R. J. Furnstahl, H.‐W. Hammer

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.

R. J. Furnstahl, H.‐W. Hammer, S. J. Puglia