Spin systems are described by the exchange interaction between the spins, the Zeeman interaction with an external magnetic field, and the spin-orbit interaction. In these systems we can often find magnetic field values where the ground state is degenerate. Often these are described as Weyl points or diabolical points, and they carry topological charge. We point out that in general, the number of these points can depend on the system parameters [1], moreover, the degeneracies are not necessarily isolated points, but can also form a closed curve or a closed surface [2]. We give an analytical formula for the locations of the ground-state degeneracies, and we calculate the topological charge distributions of the possible geometrical patterns, and investigate their stability. Our findings are relevant for spin qubit control and readout in double (or multiple) quantum dot systems.

[1] Z. Scherübl et al., Comms. Phys. 2, 108 (2019).
[2] Gy. Frank et al., https://arxiv.org/abs/1910.02831