Landau Fermi Liquid Picture of Spin Density Functional Theory: Strutinsky Approach to Quantum Dots

TL;DR

This paper introduces a Strutinsky approximation to analyze quantum dot energies and spins within spin density functional theory, revealing a Landau Fermi liquid perspective and matching statistical properties of full SDFT calculations.

Contribution

It presents a novel Strutinsky approach to approximate SDFT results, providing a Fermi liquid interpretation and enabling comparison with the universal Hamiltonian.

Findings

Strutinsky approximation achieves ~5% accuracy for large irregular dots.

Statistical analysis shows similarity between Strutinsky and full SDFT results.

The approach offers a Fermi liquid framework for understanding spin density functional theory.

Abstract

We analyze the ground state energy and spin of quantum dots obtained from spin density functional theory (SDFT) calculations. First, we introduce a Strutinsky-type approximation, in which quantum interference is treated as a correction to a smooth Thomas-Fermi description. For large irregular dots, we find that the second-order Strutinsky expressions have an accuracy of about 5 percent compared to the full SDFT and capture all the qualitative features. Second, we perform a random matrix theory/random plane wave analysis of the Strutinsky SDFT expressions. The results are statistically similar to the SDFT quantum dot statistics. Finally, we note that the second-order Strutinsky approximation provides, in essence, a Landau Fermi liquid picture of spin density functional theory. For instance, the leading term in the spin channel is simply the familiar exchange constant. A direct comparison between SDFT and the perturbation theory derived ``universal Hamiltonian'' is thus made possible.