On the degeneracy of ordered ground state configurations of the aspherical Gaussian core model

TL;DR

This paper proves that the ground state configurations of parallel ellipsoidal particles with Gaussian interactions are infinitely degenerate, originating from symmetric configurations through stretching and rotation, impacting the understanding of nematic particle arrangements.

Contribution

It provides a rigorous proof of the infinite degeneracy of ground states for Gaussian core nematics, linking them to symmetric configurations via stretching and rotation.

Findings

Ground states are infinitely degenerate.

Configurations derive from symmetric states through stretching and rotation.

Implications for nematic particle ground state searches.

Abstract

We provide rigorous evidence that the ordered ground state configurations of a system of parallel oriented, ellipsoidal particles, interacting via a Gaussian interaction (termed in literature as Gaussian core nematics) {\it must} be infinitely degenerate: we have demonstrated that these configurations originate from the related ground state configuration of the corresponding symmetric Gaussian core system via a suitable stretching operation of this lattice in combination with an arbitrary rotation. These findings explain related observations in former investigations, which then remained unexplained. Our conclusions have far reaching consequences for the search of ground state configurations of other nematic particles.