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

在准一维几何中用相互作用的玻色子和费米子进行量子气体实验，可以通过几种方式获得拓扑性质。首先，磁通阶梯是包含量子霍尔物理学（如霍夫施塔特模型）的典型二维系统的薄环面极限。在阶梯极限中，相互作用对边缘态、输运和非平衡性质的影响可以在实验和理论计算中进行研究，从而可以进行直接比较。第二，一维超晶格的实验实现了拓扑电荷和自旋泵。第三，单粒子不变量的扩展到多体的情况下，可以探索的情况下，保护拓扑绝缘体。该项目的目标是研究这些装置中的多体效应，并阐明在存在短程相互作用、无序和最先进实验的现实条件下，拓扑电荷泵和通量阶梯的量子相位的稳定性。非平衡物理将发挥重要作用，在具有不同拓扑性质的相之间的量子猝灭的背景下以及在实际实验方案中用于状态准备和加载过程。将与研究这些问题的实验小组建立密切联系。虽然电荷泵在低频范围内运行以确保绝热性，但我们还将致力于开发新的方案，用于在中频和高频下推导周期性驱动系统的有效哈密顿量，利用流量方程方法。

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.