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 finite many-body systems. 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.