Density-functional theory of the trapped two-dimensional Fermi gas in the unitary regime

Abstract

A recent paper by T. Papenbrock [Phys. Rev. A 72, 041602(R) (2005)] suggests that a determination of the universal factor ${\ensuremath{\xi}}_{3\mathrm{D}}$ for a harmonically trapped, unpolarized dilute Fermi gas in the unitary regime may be obtained within the framework of a simple density-functional theory (DFT). One of the key results of that work is an estimate for the universal factor ${\ensuremath{\xi}}_{3\mathrm{D}}\ensuremath{\approx}0.54$, which is within 20% of the generally accepted quantum Monte Carlo simulation value of ${\ensuremath{\xi}}_{3\mathrm{D}}=0.44\ifmmode\pm\else\textpm\fi{}0.01$. Motivated by this result, this report investigates the determination of the universal factor ${\ensuremath{\xi}}_{2\mathrm{D}}$ for a two-dimensional trapped Fermi gas, and suggests that the simple DFT approach of Papenbrock provides an exact result of ${\ensuremath{\xi}}_{2\mathrm{D}}=1$ in two dimensions.