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

Privitera, Antonio; Capone, Massimo; Castellani, Claudio

doi:10.1103/PHYSREVB.81.014523

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

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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 (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 ofmore »« less

Authors:

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

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

Publication Date:: Fri Jan 01 00:00:00 EST 2010

OSTI Identifier:: 21366648

Resource Type:: Journal Article

Journal Name:: Physical Review. B, Condensed Matter and Materials Physics

Additional Journal Information:: Journal Volume: 81; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevB.81.014523; (c) 2010 The American Physical Society; Journal ID: ISSN 1098-0121

Country of Publication:: United States

Language:: English

Subject:: 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

Citation Formats


                    Privitera, Antonio, Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt am Main, Capone, Massimo, ISC-CNR, Via dei Taurini 19, I-00185 Roma, and Castellani, Claudio. Finite-density corrections to the unitary Fermi gas: A lattice perspective from dynamical mean-field theory.  United States: N. p., 2010. 
        Web.  doi:10.1103/PHYSREVB.81.014523.

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                    Privitera, Antonio, Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt am Main, Capone, Massimo, ISC-CNR, Via dei Taurini 19, I-00185 Roma, & Castellani, Claudio. Finite-density corrections to the unitary Fermi gas: A lattice perspective from dynamical mean-field theory.  United States.  https://doi.org/10.1103/PHYSREVB.81.014523

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                    Privitera, Antonio, Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt am Main, Capone, Massimo, ISC-CNR, Via dei Taurini 19, I-00185 Roma, and Castellani, Claudio. 2010.  
        "Finite-density corrections to the unitary Fermi gas: A lattice perspective from dynamical mean-field theory".  United States.  https://doi.org/10.1103/PHYSREVB.81.014523.

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@article{osti_21366648,

  title        = {Finite-density corrections to the unitary Fermi gas: A lattice perspective from dynamical mean-field theory},

  author       = {Privitera, Antonio and Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt am Main and Capone, Massimo and ISC-CNR, Via dei Taurini 19, I-00185 Roma and Castellani, Claudio},

  abstractNote = {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.},

  doi          = {10.1103/PHYSREVB.81.014523},

  url          = {https://www.osti.gov/biblio/21366648},
  journal      = {Physical Review. B, Condensed Matter and Materials Physics},

  issn         = {1098-0121},

  number       = 1,

  volume       = 81,

  place        = {United States},

  year         = {Fri Jan 01 00:00:00 EST 2010},

  month        = {Fri Jan 01 00:00:00 EST 2010}

}

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