Topologically protected ground state degeneracies in an interacting two-spin system

We theoretically study geometrical and topological aspects of a simple, yet experimentally relevant quantum magnet: two localized interacting electrons subject to spin-orbit coupling [1]. In our topological considerations the parameter space is the external magnetic field, and we search for the degeneracies of the ground state. These degeneracies carry a topological charge, which is the Chern number obtained as the integral of the ground-state Berry curvature for a surface containing them. The Hamiltonian is simple enough to find degeneracies analytically, however complex enough to have a rich geometrical classification [2]. We identify ten different possible geometrical patterns formed by these degeneracies and study their stability under small perturbations of the Hamiltonian. We expect that near-term experiments will be able to measure the Berry curvature and the Chern number associated to these degeneracy patterns [3].

References
[1] Z. Scherübl et al., Communication Physics, 2 108 (2019).
[2] Gy. Frank et al., Phys. Rev. B, 101 245409 (2020).
[3] V. Gritsev et al., PNAS, 109 (17) 6457-6462 (2020).