Geometrical Perspective on Spin-Lattice Density-Functional Theory

TL;DR

This paper introduces a geometrical framework for spin-lattice density-functional theory, providing new insights into the Hohenberg-Kohn theorem and v-representability, with applications to impurity models and time-dependent phenomena.

Contribution

It presents a novel geometrical approach to fundamental concepts in spin-lattice density-functional theory, expanding understanding of degeneracy regions and v-representability.

Findings

Geometrical description of the Hohenberg-Kohn theorem

Application to Anderson impurity model

Analysis of adiabatic and time-dependent cases

Abstract

A recently developed viewpoint on the fundamentals of density-functional theory for finite interacting spin-lattice systems that centers around the notion of degeneracy regions is presented. It allows for an entirely geometrical description of the Hohenberg-Kohn theorem and v-representability. The phenomena receive exemplification by an Anderson impurity model and other small-lattice examples. The case of adiabatic change and the time-dependent setting are examined as well.