Abstract: In this talk, I will present new exotic topologies involving non-Abelian braiding of band nodes in multi-gap non-interacting systems. I will demonstrate new anomalous topological phases in out-of-equilibrium settings with no static counterparts, as well as ways for quantum simulators to probe them. Furthermore, many of these topological evaluations are related to the underlying quantum geometry, for which the Bloch sphere constitutes a paradigmatic example in the minimal two-level models. I will here introduce a geometric description for generic N-level systems in terms of a nested structure comprising spheres, which opens up a new avenue for the interpretation of the topological classification and the dynamical illustration of multi-level systems as well as the design of new experimental probes.
The College of Arts