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 $|k_{\mathrm{F}}{a}_s|\lesssim 0.5$.

arXiv comment6 pages, 2 figures; v2: minor improvements in text, references updated, matches published version

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• Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion
• Application of an ab-initio-inspired energy density functional to nuclei: impact of the effective mass and the slope of the symmetry energy on bulk and surface properties
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• Ground state energy of the polarized diluted gas of interacting spin $1/2$ fermions
• Bayesian inference of neutron star crust properties using an ab initio-benchmarked meta-model
• Toward precision Fermi liquid theory in two dimensions
• Constrained extrapolation problem and order-dependent mappings
• Third order corrections to the ground state energy of the gas of spin $s$ fermions with arbitrary densities of different spin projections
• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods
• Multicomponent Fermi systems at low densities