Transdimensional equivalence of universal constants for Fermi gases at unitarity

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.

arXiv comment4 pages, 3 figures, 1 Table; minor revisions to the title, abstract and main text

References in corpus (20)

• Theory of ultracold Fermi gases
• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Experimental Study of the BEC-BCS Crossover Region in Lithium 6
• Creation of ultracold molecules from a Fermi gas of atoms
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Decay of an ultracold fermionic lithium gas near a Feshbach resonance
• Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions
• Universal Fermi gases in mixed dimensions
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• A lattice theory for low energy fermions at finite chemical potential
• Density-functional theory for fermions in the unitary regime
• Universal four-component Fermi gas in one dimension
• Lattice theory for nonrelativistic fermions in one spatial dimension

Cited by in corpus (6)

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• Unitary $p$-wave Fermi gas in one dimension
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• Thermodynamics and static response of anomalous 1D fermions via quantum Monte Carlo in the worldline representation
• Few-body physics on a space-time lattice in the worldline approach
• Numerical study of unitary fermions in one spatial dimension