Density-Functional Theory on Graphs

TL;DR

This paper explores the application of density-functional theory to finite lattice systems modeled as graphs, revealing limitations of the Hohenberg-Kohn theorem and providing conditions for unique v-representability.

Contribution

It demonstrates the failure of the Hohenberg-Kohn theorem in graph-based systems and establishes conditions for ground state v-representability in these models.

Findings

Hohenberg-Kohn theorem does not hold generally for graph systems

Almost all densities are v-representable under certain conditions

Pure-state constrained-search functional is non-convex

Abstract

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of the density-potential mapping can be won. We give precise conditions for a ground state to be uniquely v-representable and are able to prove that this property holds for almost all densities. A set of examples illustrates the theory and demonstrates the non-convexity of the pure-state constrained-search functional.