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

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, $\mathcal{S}$. Both for $\mathcal{S}=+1$ and $\mathcal{S}=-1$, 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.

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Cited by in corpus (7)

• All-electrical control of hole singlet-triplet spin qubits at low leakage points
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
• Exchange interaction of hole-spin qubits in double quantum dots in highly anisotropic semiconductors
• Classification and magic magnetic-field directions for spin-orbit-coupled double quantum dots
• Stability of Weyl node merging processes under symmetry constraints
• Topological charge distributions of an interacting two-spin system
• The geometry of the Hermitian matrix space and the Schrieffer--Wolff transformation