Uniform magnetic fields in density-functional theory

TL;DR

This paper develops a new density-functional formalism called LDFT for uniform magnetic fields, bridging the gap between traditional DFT and CDFT, with simplified theoretical foundations and key properties proven.

Contribution

The paper introduces LDFT, an intermediate formalism for uniform magnetic fields, with new theoretical results and simplified analogues to CDFT.

Findings

Proves N-representability and Hohenberg-Kohn-like mappings in LDFT.

Establishes existence of minimizers in the constrained-search formulation.

Discusses the additivity of energy in LDFT versus CDFT.

Abstract

We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional Density Functional Theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term LDFT, the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre--Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogues in LDFT. We prove results concerning $N$-representability, Hohenberg--Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analogue to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.