Topological charge distributions of an interacting two-spin system

Abstract

Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the degeneracy points form a nodal loop or a nodal surface in the magnetic parameter space, similarly to such structures discovered in the band structure of topological semimetals. Key results of our work are that (1) we determine the topological charge distribution along these degeneracy geometries and (2) we show that these nonpointlike degeneracy patterns can be obtained not only by fine-tuning but they can be stabilized by spatial symmetries. Since simple spin systems such as the one studied here are ubiquitous in condensed-matter setups, we expect that our findings, and the physical consequences of these nontrivial degeneracy geometries, are testable in experiments with quantum dots, molecular magnets, and adatoms on metallic surfaces.

Birth Quota of Non-Generic Degeneracy Points

“…Our results are not exclusive to Weyl points in three dimensions (3D), we also obtain an analogous result for two-dimensional (2D) crystals with chiral symmetry illustrated on the example of bilayer graphene, as well as a minimal example in 1D. Even though we showcase the power of these results on electronic band structures of solids, they are more generic, applicable to quantum systems controlled by external parameters, such as interacting spin systems [7][8][9][10][11] or quantum circuits [12,13].…”