Artificial Gauge Fields versus Interaction Effects

人工规范场与相互作用效应

• 批准号: 318596974
• 负责人: Professorin Dr. Karyn Le Hur, Ph.D.
• 金额: --
• 依托单位: Centre de Physique Théorique (CPHT)
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/318596974?language=en
• 关键词: Artificial; Gauge; Fields; versus; Interaction

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.

近几十年来，随着量子霍尔效应、霍尔丹模型和量子自旋霍尔效应的实现，拓扑相的探索已经成为一个巨大的挑战，这更普遍地导致了拓扑绝缘体、拓扑超导体和具有马约拉纳费米子的磁系统。在这个项目中，主要目标是在相互作用存在的情况下发现和表征新的拓扑相，并通过在光学晶格中实现人工规范场，提出在超冷原子中的实际应用。我们将研究费米子和玻色子，从弱相互作用到强相互作用，然后导致具有有趣磁性的莫特物理和分数量子霍尔相。我们在新的界面和混合系统中引入了两个与拓扑邻近效应相关的新平台。第二阶段的项目分为四个班级，展示了我们在这个研究单元中的合作：阶梯和导线拓扑模型，准二维系统中的相互作用拓扑相和拓扑邻近效应，拓扑表征和新探针，时间相关现象和光物质耦合。在方法方面，将努力利用量子场论技术和随机方法，并辅以一些数值方法。为了解决存在相互作用时相关哈密顿量的性质，随机方法和半经典分析将与数值对角化和有效的Floquet理论进行比较。