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arXiv · 1210.3104

Transdimensional equivalence of universal constants for Fermi gases at unitarity

Michael G. Endres
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Abstract

I present lattice Monte Carlo calculations for a universal four-component Fermi gas confined to a finite box and to a harmonic trap in one spatial dimension. I obtain the values xi_1d = 0.370(4) and xi_1d = 0.372(1), respectively, for the Bertsch parameter, a nonperturbative universal constant defined as the (square of the) energy of the untrapped (trapped) system measured in units of the free gas energy. The Bertsch parameter for the one-dimensional system is consistent to within ~1% uncertainties with the most recent numerical and experimental estimates of the analogous Bertsch parameter for a three-dimensional spin-1/2 Fermi gas at unitarity. The finding suggests the intriguing possibility that there exists a universality between two conformal theories in different dimensions. To lend support to this study, I also compute continuum extrapolated ground state energies for four and five fermions confined to a harmonic trap and demonstrate the restoration of a Virial theorem in the continuum limit. The continuum few-body energies obtained are consistent with exact analytical calculations to within ~1.0% and ~0.25% statistical uncertainties, respectively.

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Michael G. Endres. 2012-12-24. Transdimensional equivalence of universal constants for Fermi gases at unitarity. https://doi.org/10.1103/physrevlett.109.250403

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