Finite-density corrections to the unitary Fermi gas: A lattice perspective from dynamical mean-field theory

Journal Article · Fri Jan 01 00:00:00 EST 2010 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.81.014523· OSTI ID:21366648

Privitera, Antonio ^[1]; Capone, Massimo ^[1]; Castellani, Claudio ^[1]

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1. CRS SMC, CNR-INFM and Dipartimento di Fisica, Universita di Roma 'La Sapienza', Piazzale Aldo Moro 2, I-00185 Roma (Italy)

We investigate the approach to the universal regime of the dilute unitary Fermi gas as the density is reduced to zero in a lattice model. To this end we study the chemical potential, superfluid order parameter and internal energy of the attractive Hubbard model in three different lattices with densities of states (DOSs) which share the same low-energy behavior of fermions in three-dimensional free space: a cubic lattice, a 'Bethe lattice' with a semicircular DOS, and a 'lattice gas' with parabolic dispersion and a sharp energy cutoff that ensures the normalization of the DOS. The model is solved using dynamical mean-field theory, that treats directly the thermodynamic limit and arbitrarily low densities, eliminating finite-size effects. At densities on the order of one fermion per site the lattice and its specific form dominate the results. The evolution to the low-density limit is smooth and it does not allow to define an unambiguous low-density regime. Such finite-density effects are significantly reduced using the lattice gas, and they are maximal for the three-dimensional cubic lattice. Even though dynamical mean-field theory is bound to reduce to the more standard static mean field in the limit of zero density due to the local nature of the self-energy and of the vertex functions, it compares well with accurate Monte Carlo simulations down to the lowest densities accessible to the latter.

• OSTI ID: 21366648
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 81, Issue 1; Other Information: DOI: 10.1103/PhysRevB.81.014523; (c) 2010 The American Physical Society; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
CORRECTIONS
CUBIC LATTICES
DENSITY
DISPERSIONS
FERMI GAS
FERMIONS
HUBBARD MODEL
LATTICE FIELD THEORY
MEAN-FIELD THEORY
MONTE CARLO METHOD
ORDER PARAMETERS
SELF-ENERGY
SUPERFLUIDITY
THREE-DIMENSIONAL CALCULATIONS
VERTEX FUNCTIONS
CALCULATION METHODS
CONSTRUCTIVE FIELD THEORY
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
DIMENSIONLESS NUMBERS
ENERGY
EVALUATION
FIELD THEORIES
FUNCTIONS
MATHEMATICAL MODELS
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
SIMULATION