Geometrical perspective on spin-lattice density-functional theory.

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Computational chemistry

Background:

• Density-functional theory (DFT) is a cornerstone for electronic structure calculations.
• Understanding DFT fundamentals in finite, interacting spin-lattice systems remains an active research area.
• Existing approaches may lack a unified geometrical framework.

Purpose of the Study:

• To present a novel geometrical viewpoint on the fundamentals of density-functional theory.
• To explore the concept of degeneracy regions within finite interacting spin-lattice systems.
• To provide a geometrical interpretation of the Hohenberg-Kohn theorem and v-representability.

Main Methods:

• Development of a new theoretical framework based on degeneracy regions.
• Application of the framework to exemplify phenomena in specific models.
• Examination of adiabatic and time-dependent scenarios.

Main Results:

• A geometrical description of the Hohenberg-Kohn theorem and v-representability is achieved.
• The Anderson impurity model and small-lattice systems are used to illustrate the theory.
• The framework is extended to address adiabatic changes and time-dependent situations.

Conclusions:

• The degeneracy region viewpoint offers a powerful geometrical understanding of DFT for spin systems.
• This approach unifies key concepts and provides a versatile tool for analysis.
• The presented framework has implications for both static and dynamic properties of quantum systems.