A discrete density matrix theory for atoms in strong magnetic fields

TL;DR

This paper introduces a discrete density matrix (DDM) functional for analyzing the ground state properties of heavy atoms in strong magnetic fields, simplifying the density matrix approach by using angular momentum quantum numbers.

Contribution

It develops a new DDM functional that replaces the perpendicular variable with angular momentum quantum numbers, extending the density matrix theory for atoms in strong magnetic fields.

Findings

The DDM functional accurately reproduces the ground state energy.

It relates to the lowest Landau band quantum mechanics.

The theory accounts for Coulomb interaction errors.

Abstract

This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to infinity with the magnetic field B satisfying B >> Z^{4/3} all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy.