Ground state energy of unitary fermion gas with the Thomson Problem approach

Abstract

The dimensionless universal coefficient $\xi$ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson Problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be $\xi =4/9$. The energy gap is $Δ=\frac{{5}{18}{k_f^2}/(2m)$.

Identical to published version with revisions according to comments

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Cited by in corpus (14)

• The ground state energy at unitarity
• Lattice methods for strongly interacting many-body systems
• Lattice Monte Carlo calculations for unitary fermions in a finite box
• Precision benchmark calculations for four particles at unitarity
• Quantum rearrangement and self-consistent BCS-BEC crossover thermodynamics
• The symmetric heavy-light ansatz
• Superfluid Condensate Fraction and Pairing Wave Function of the Unitary Fermi Gas
• The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics
• The virial equation of state for unitary fermion thermodynamics with non-Gaussian correlations
• Quantum Many-Body Calculations using Body-Centered Cubic Lattices
• Density functional theory of the trapped Fermi gas in the unitary regime
• Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities
• Determination of Landau Fermi-liquid parameters of strongly interacting fermions by means of a nonlinear scaling transformation
• An Effective Series Expansion to the Equation of State of Unitary Fermi Gases