Artificial Gauge Fields versus Interaction Effects

随着量子霍尔效应、量子自旋霍尔效应和量子自旋霍尔效应的实现，拓扑相的研究在过去的几十年里一直是一个巨大的挑战，拓扑绝缘体、拓扑超导体和含有马约拉纳费米子的磁性系统也随之出现。在这个项目中，主要的目标是发现和表征新的拓扑相位存在的相互作用，并建议真实的应用在超冷原子通过实施人工规范场的光学晶格。我们将研究费米子和玻色子从弱相互作用制度的强关联，然后导致莫特物理与有趣的磁性和分数量子霍尔相位。我们介绍了两个新的平台，在新的接口和混合系统的拓扑邻近效应。第二阶段的项目分为四类，展示了我们在这个研究单位内的合作：梯子和线拓扑模型，相互作用的拓扑相位和准二维系统中的拓扑邻近效应，拓扑表征和新探针，时间依赖现象和光物质耦合。关于方法，将努力做量子场论技术和随机方法，辅以一些数值方法。为了解决在相互作用的存在下，随机方法和半经典分析的时间相关的哈密顿性质将与数值对角化和有效的Floquet理论进行比较。

The quest of topological phases has been a great challenge the last decades with the realization of quantum Hall effects, Haldane model and quantum spin Hall effect leading more generally to topological insulators, topological superconductors and magnetic systems with Majorana fermions. In this project, the primary goal is to find and characterize new topological phases in the presence of interactions and to suggest real applications in ultra-cold atoms through the implementation of artificial gauge fields in optical lattices. We will study fermions and bosons from the weakly-interacting regime to the strongly-correlated one, then leading to Mott physics with interesting magnetic properties and to fractional quantum Hall phases. We introduce two new platforms in relation with topological proximity effects in novel interfaces and hybrid systems. The project for the second period is organized in four classes, demonstrating our collaborations within this Research Unit: ladders and wire topological models, interacting topological phases and topological proximity effects in quasi-two-dimensional systems, topological characterization and new probes, time-dependent phenomena and light-matter coupling. Regarding the methodology, an effort will be done on quantum field theory techniques and stochastic approaches complemented by some numerical approaches. To tackle properties of timedependent Hamiltonians in the presence of interactions, stochastic approaches and semi-classical analysis will be compared with numerical diagonalizations and effective Floquet theories.