Topological order beyond the equilibrium ground state: driven quantum matter and magnon excitation spectra

ended

With the discovery of topological order, condensed matter physics has witnessed a revolution in how phases of matter ought to be defined and characterized. Unlike spins aligning in a magnet, topological phases are not classified by symmetry breaking but instead require nonlocal invariants that relate to the mathematical domain of topology. This theme took a turn with the finding that even common electronic band structures can feature topological invariants in the presence of appropriate symmetries. Ever since, many such symmetry protected topological (SPT) states have been predicted and arranged into a unifying table. These developments have been accompanied by the actual realization of various topological band insulators that feature striking properties including protected metallic edge states and proposed exotic fractionalized excitations, which may provide a route to fault-tolerant topological quantum computing. Now, the field is approaching a new exciting turning point as indications are emerging that other parts of the modern 'Mendeleev table' exist involving band structures that do not pertain to equilibrium ground states. On the verge of this milestone, this project will take a pioneering role and investigate such SPT phases in the context of periodically driven quantum systems and magnon excitation spectra. The objective is to uncover the underlying general classification principles, which will provide a guide to engineering novel states and accordingly new physics. To this end, we will apply a multidisciplinary approach combining state-of-the-art handles on SPT order, insights from analytically tractable models and numerics. In particular, we envision that naturally present crystal symmetries will play a prominent role here -one that has yet to be appreciated- much as they do in equilibrium SPTs. Together with a complementary generalization of physical observables, we expect this action to pave the way to a new chapter in the success story of SPT phases.