Density-functional theory for fermions in the unitary regime

Abstract

In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the free Fermi gas with a proportionality constant $\xi$. We use a simple density functional parametrized by an effective mass and the universal constant $\xi$, and employ Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\xi =0.42$ and a rather large effective mass. Our approach is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.

5 pages, 2 figures

References in corpus (3)

• Observation of Bose-Einstein Condensation of Molecules
• Collective excitations of a degenerate gas at the BEC-BCS crossover
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction

Cited by in corpus (11)

• Unitary Fermi Gas in a Harmonic Trap
• The ground state energy at unitarity
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory
• On Non-Relativistic Conformal Field Theory and Trapped Atoms: Virial Theorems and the State-Operator Correspondence in Three Dimensions
• Fermionic ground state at unitarity and Haldane Exclusion Statistics
• Fermions at unitarity and Haldane Exclusion Statistics
• Density-functional theory for the pairing Hamiltonian
• Energy functional for the three-level Lipkin model
• Density functional theory of the trapped Fermi gas in the unitary regime
• The Fermionic Density-functional at Feshbach Resonance