Ground-state energy of the unitary Fermi gas from the epsilon expansion

TL;DR

This paper refines the estimate of the ground-state energy ratio of the unitary Fermi gas to a noninteracting Fermi gas using advanced epsilon expansion techniques, achieving a more accurate value consistent with previous results.

Contribution

It introduces the next-to-next-to-leading-order (NNLO) epsilon expansion to improve the calculation of the energy ratio near two dimensions and employs Pade approximants for interpolation.

Findings

Estimated xi=0.360±0.020 in three dimensions

NNLO corrections are large but consistent with previous NLO results

Interpolation methods effectively bridge different spatial dimensions

Abstract

We update the ground-state energy ratio of unitary Fermi gas to noninteracting Fermi gas (xi) from the epsilon expansion by including the next-to-next-to-leading-order (NNLO) term near two spatial dimensions. Interpolations of the NNLO epsilon expansions around four and two spatial dimensions with the use of Pade approximants give xi=0.360+/-0.020 in three dimensions with the uncertainty due to different interpolation functions. This value is consistent with the previous interpolations of the NLO epsilon expansions xi=0.377+/-0.014 in spite of the large NNLO corrections.