Magnetic degeneracy points in interacting two-spin systems: geometrical patterns, topological charge distributions, and their stability

TL;DR

This paper explores the geometrical arrangements and topological stability of degeneracy points in a simple two-electron quantum magnet with spin-orbit coupling, revealing stable configurations and bifurcation structures.

Contribution

It identifies ten possible geometrical patterns of degeneracy points and analyzes their stability depending on the sign of the determinants of the g-tensors, providing new insights into topological degeneracies.

Findings

Ten geometrical patterns of degeneracy points identified.

Stable configurations depend on the sign of the g-tensor determinants.

Presence of bifurcation surfaces separating stable and unstable regions.

Abstract

Spectral degeneracies of quantum magnets are often described as diabolical points or magnetic Weyl points, which carry topological charge. Here, we study a simple, yet experimentally relevant quantum magnet: two localized interacting electrons subject to spin-orbit coupling. In this setting, the degeneracies are not necessarily isolated points, but can also form a line or a surface. We identify ten different possible geometrical patterns formed by these degeneracy points, and study their stability under small perturbations of the Hamiltonian. Stable structures are found to depend on the relative sign of the determinants of the two $g$-tensors, $\cal S$. Both for ${\cal S}=+1$ and ${\cal S}=-1$, two stable configurations are found, and three out of these four configurations are formed by pairs of Weyl points. These stable regions are separated by a surface of almost stable configurations, with a structure akin to co-dimension one bifurcations.