New Frontiers in Topology, Quantum Geometry and Quantum Simulations
F. Nur Ünal
Abstract: Topologically protected phases profit from connections with mathematical principles to characterize illustrious physical behaviours in tangible systems. State-of-the-art quantum simulators provide a versatile platform for exploring these phenomena at a fundamental level, even providing the opportunity for observing the ‘knots’ wave functions tie during their evolution. I will talk about new exotic topologies involving non-Abelian braiding of band nodes in multi-gap systems, and demonstrate new phases in out-of-equilibrium settings with no static counterparts as well as ways for quantum simulators to probe them. I will further introduce new geometric descriptions for N-level systems in terms of a nested structure comprising spheres, opening 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.