Uniform magnetic fields in density-functional theory

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Theoretical Chemistry

Background:

• Density-functional theory (DFT) is a cornerstone for electronic structure calculations.
• Current-Density Functional Theory (CDFT) extends DFT to include magnetic fields but presents theoretical complexities.
• A need exists for a formalism that bridges DFT and CDFT, offering a simpler yet powerful approach for magnetic field problems.

Purpose of the Study:

• To develop a novel density-functional formalism, termed linear vector potential-DFT (LDFT).
• To establish LDFT as an intermediate theory between conventional DFT and CDFT for uniform external magnetic fields.
• To investigate and simplify theoretical issues inherent in CDFT within the LDFT framework.

Main Methods:

• Construction of a density-functional formalism incorporating density, canonical momentum, and paramagnetic moment as basic variables.
• Development of both a constrained-search formulation and a convex formulation using Legendre-Fenchel transformations.
• Analysis of theoretical properties including N-representability, Hohenberg-Kohn-like mappings, and gauge invariance analogs.

Main Results:

• LDFT is established as a viable intermediate theory for uniform magnetic fields.
• Theoretical challenges in CDFT, such as N-representability and gauge invariance, are shown to have simplified analogs in LDFT.
• Existence of minimizers in the constrained-search formulation is proven.
• The distinct nature of energy additivity for non-interacting subsystems in LDFT versus CDFT is discussed.

Conclusions:

• LDFT offers a simplified yet rigorous framework for studying systems under uniform magnetic fields.
• The developed formalism provides new insights into the theoretical underpinnings of magnetic field effects in density-functional theory.
• LDFT serves as a valuable theoretical tool, potentially simplifying complex calculations and analyses in quantum chemistry and condensed matter physics.