Large and exact quantum degeneracy in a Skyrmion magnet

TL;DR

This paper demonstrates that a class of topological Skyrmion ground states in certain magnetic systems exhibit large degeneracy and robustness against quantum fluctuations, due to their saturation of a Bogomolny inequality, with potential realization in quantum Hall ferromagnets.

Contribution

It identifies a family of Skyrmion ground states with persistent degeneracy and stability, linking topological properties to quantum robustness and suggesting experimental realizations.

Findings

Ground states are classically degenerate and remain so quantum mechanically.

These states are not affected by quantum fluctuations due to Bogomolny saturation.

Potential realization in quantum Hall ferromagnets.

Abstract

We identify a large family of ground states of a topological Skyrmion magnet whose classical degeneracy persists to all orders in a semiclassical expansion. This goes along with an exceptional robustness of the concomitant ground state configurations, which are not at all dressed by quantum fluctuations. We trace these twin observations back to a common root: this class of topological ground states saturates a Bogomolny inequality. A similar phenomenology occurs in high-energy physics for some field theories exhibiting supersymmetry. We propose quantum Hall ferromagnets, where these Skyrmions configurations arise naturally as ground states away from integer filling, as the best available laboratory realisations.