Ground-state degeneracies leave recognizable topological scars in the one-particle density

TL;DR

This paper demonstrates that exact Kohn-Sham density functional theory can detect and characterize ground-state degeneracies and their associated topological features, such as Berry phases, through detailed density 'scars' on a parameter manifold.

Contribution

It provides theoretical evidence that ground-state degeneracies leave topological signatures in the density, enabling their detection and characterization within exact KS-DFT.

Findings

Ground-state degeneracies create topological scars in the density.

Exact KS-DFT can identify degeneracy positions and Berry phases.

Density scars encode detailed topological information.

Abstract

In Kohn-Sham density functional theory (KS-DFT) a fictitious system of non-interacting particles is constructed having the same ground-state (GS) density as the physical system of interest. A fundamental open question in DFT concerns the ability of an exact KS calculation to spot and characterize the GS degeneracies in the physical system. In this article we provide theoretical evidence suggesting that the GS density, as a function of position on a 2D manifold of parameters affecting the external potential, is "topologically scarred" in a distinct way by degeneracies. These scars are sufficiently detailed to enable determination of the positions of degeneracies and even the associated Berry phases. We conclude that an exact KS calculation can spot and characterize the degeneracies of the physical system.