Finite-density corrections to the Unitary Fermi gas: A lattice perspective from Dynamical Mean-Field Theory

Abstract

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 (DOS) 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 cut-off 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 of 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.

9 pages, 8 figures

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Cited by in corpus (19)

• Local Electronic Correlation at the Two-Particle Level
• Lattice methods for strongly interacting many-body systems
• Low temperature properties of the infinite-dimensional attractive Hubbard model
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Dynamical vertex approximation for the attractive Hubbard model
• Valence-band satellite in the ferromagnetic nickel: LDA+DMFT study with exact diagonalization
• Population imbalanced lattice fermions near the BCS-BEC crossover: II. The FFLO regime and its thermal signatures
• Population imbalanced lattice fermions near the BCS-BEC crossover: I.The breached pair and metastable FFLO phases
• Numerical study of the unitary Fermi gas across the superfluid transition
• Strong coupling s-wave superconductors in the extreme Pauli limit: I.The breached pair and metastable FFLO phases
• Inhomogeneous BCS-BEC crossover for trapped cold atoms in optical lattices
• Improved lattice operators for non-relativistic fermions
• Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity
• Lattice approaches to dilute Fermi gases: Legacy of broken Galilean invariance
• Interface and bulk superconductivity in superconducting heterostructures with enhanced critical temperatures
• Coexistence of $s$-wave superconductivity and phase separation in the half-filled extended Hubbard model with attractive interactions
• Zero density limit extrapolation of the superfluid transition temperature in a unitary atomic Fermi gas on a lattice
• Thermal transitions, pseudogap behavior and BCS-BEC crossover in Fermi-Fermi mixtures
• Proton fraction in neutron star matter: Dynamical mean-field approach