Density Functional Theory for a Confined Fermi System with Short-Range Interaction

Abstract

Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Representative results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates.

36 pages, 20 figures, RevTeX4

References in corpus (20)

• Resonance superfluidity in a quantum degenerate Fermi gas
• Density Functional Theory -- an introduction
• Prospect of creating a composite fermi/bose superfluid
• Effective Field Theory of Nuclear Forces
• All-Optical Production of a Degenerate Fermi Gas
• Effective action approach to strongly correlated fermion systems
• Effective Field Theory for Dilute Fermi Systems
• Hartree Fock Calculations in the Density Matrix Expansion Approach
• Interacting Fermi gas in a Harmonic Trap
• Parameter Counting in Relativistic Mean-Field Models
• Quantum Corrections to the Ground State of a Trapped Bose-Einstein Condensate
• What is Renormalization?
• Effective action and density functional theory
• Renormalization Effects in a Dilute Bose Gas
• Field Redefinitions at Finite Density
• Quasi-Local Density Functional Theory and its Application within Extended Thomas-Fermi Approximation
• Dynamical Mean Field Theory and Electronic Structure Calculations
• Effective Field Theory for Fermi Systems in a large N expansion
• Effective actions of local composite operators --- case of ${\phi }^4$ theory, itinerant electron model, and QED
• An Effective Potential for Composite Operators

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• Intrinsic-Density Functionals
• Relativistic nuclear energy density functional constrained by low-energy QCD
• Effect of impurity on the determination of ground-state properties of parabolic quantum dot composed of N electrons
• Density-functional theory for fermions in the unitary regime
• Symmetry energy in nuclear density functional theory
• An effective field theory for coupled-channel scattering
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Density Matrix Expansion for Low-Momentum Interactions
• Effective density functionals beyond mean field
• The Kinetic Energy Density in Kohn-Sham Density Functional Theory
• Large-Scale Self-Consistent Nuclear Mass Calculations
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Effective Field Theory and Finite Density Systems
• Density Functional Theory: Methods and Problems
• Effective Field Theory for Dilute Fermions with Pairing
• Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
• Extended Skyrme interactions for transport model simulations of heavy-ion collisions
• Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study
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• Nuclear collective dynamics in the lattice Hamiltonian Vlasov method
• Single-Particle Properties from Kohn-Sham Green's Functions
• Effective 3-Body Interaction for Mean-Field and Density-Functional Theory
• Density-functional theory for the pairing Hamiltonian
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Energy functional for the three-level Lipkin model
• Nuclear structure far from stability
• Occupation number-based energy functional for nuclear masses
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• KIDS density functional for deformed nuclei: Examples of the even-even Nd isotopes
• Correlation Testing in Nuclear Density Functional Theory
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Three-Body Interactions in Many-Body Effective Field Theory