Quasi One-Dimensional Systems with Nontrivial Topology: Nonequilibrium, Transport and Edge States

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Quantum-gas experiments with interacting bosons and fermions in quasi-one dimensional geometries give access to topological properties in several ways. First, flux-ladders are the thin-torus limit of paradigmatic two-dimensional systems that host Quantum-Hall physics such as the Hofstadter model. In the ladder limit, interaction effects on edge states, transport and nonequilibrium properties can be studied both in experiments and in theoretical calculations, allowing for a direct comparison. Second, experiments with one-dimensional superlattices with commensurate wavelengths realize topological charge and spin pumps. Third, extensions of single-particle invariants to the many-body case can be explored in the case of symmetry-protected topological insulators. The goal of this project is to investigate many-body effects in these setups and to elucidate the stability of topological charge pumping and quantum phases of flux ladders in the presence of short-range interactions, disorder and realistic conditions of state-of-the-art experiments.Nonequilibrium physics will play a significant role, both in the context of quantum quenches between phases with different topological properties and for the state-preparation and loading processes in actual experimental protocols. A close contact with experimental teams working on these questions will be established. While charge pumps are operated in the low-frequency regime to ensure adiabaticity, we will also work on developing new schemes for deriving effective Hamiltonians of periodically driven systems at intermediate and high frequencies, exploiting the flow-equation method.