Calculation of ground state energy of harmonically confined two dipolar fermions

TL;DR

This paper calculates the ground state energy of two dipolar fermions in a harmonic trap using variational, Hartree-Fock, and density functional methods, comparing results to evaluate correlation effects and approximation accuracy.

Contribution

It introduces a comprehensive comparison of variational, Hartree-Fock, and density functional approaches for dipolar fermions, assessing correlation energy and approximation validity.

Findings

Correlation energy estimated by subtracting Hartree-Fock from wave function results.

Density functional theory results are compared to wave function calculations.

Assessment of local density approximation accuracy for correlation energy.

Abstract

We calculate the ground state energies of a system of two dipolar fermions trapped in a harmonic oscillator potential. The dipoles are assumed to be aligned parallel to each other. We perform the calculations of ground state energy as a function of strength of interaction between two fermions by employing variational method with Hylleraas-like explicitly correlated wave function. Furthermore, we perform calculations of ground state energy within Hartree-Fock approximation and the magnitude of correlation energy is estimated by subtracting these results from the corresponding wave function based results. We also carry out calculations of ground state energies within the realm of density functional theory by using recently reported expressions for exchange and correlation energies under local density approximation. By comparing correlated wave function based results with those obtained using density functional theory approach we examine the role of fermion-fermion correlation and assess the accuracy of local density approximation based expression for the correlation energy functional.