We study the role of electron-electron interactions near integer and abelian fractional quantum Hall (QH) transitions using composite fermion (CF) representations. Interaction effects are encapsulated in CF theories as gauge fluctuations. Without gauge fluctuations, the CF system realizes a `dual' representation of the non-interacting QH transition. With gauge fluctuations, the system is governed by a gauged nonlinear sigma model (NLSM) with a $θ-$term. While the transition is described by a strong-coupling fixed point of the NLSM, we are nevertheless able to deduce two of its properties. With $1/r$ interactions, 1) the transition has a dynamical exponent $z=1$, and 2) all transitions are `superuniversal': fractional and integer QH transitions are in the same universality class. With short-range interactions, $z=2$ and the fate of superuniversality remains unclear.
The flow of local quantum fluids: Conservation laws and vertex corrections from many-body linear-response theory with local self-energy
Institut für Quantenmaterialien und Technologien, Karlsruher Institut für Technologie（量子材料与技术研究所，卡尔斯鲁厄理工学院）；Institut für Theorie der Kondensierten Materie, Karlsruher Institut für Technologie（凝聚态理论研究所，卡尔斯鲁厄理工学院）
Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate
拓扑规范理论为某些强关联系统提供了强有力的有效描述，一个主要的例子是分数量子霍尔态的陈-西蒙斯规范理论。受控量子系统中的工程拓扑规范理论在概念和实践上都很重要，因为它将提供对具有奇异激发的系统（如任意子）的访问，而不需要强关联。在这里，我们讨论了一个计划，工程手征BF理论，拓扑规范理论的极小模型对应的陈-西蒙斯理论的一维约化，与超冷原子。利用该理论的局域守恒定律，我们将其量子哈密顿量编码为具有手征相互作用的超冷量子气体。在Edmonds等人（Phys. Rev. Lett. 110，085301（2013）），我们展示了如何在具有不平衡散射长度的拉曼耦合玻色-爱因斯坦凝聚体中实现它，正如我们最近在实验上实现的那样（Frölian等人，Nature 608，293（2022））。我们从规范理论的角度讨论了手征凝聚体的性质，并通过数值模拟评估了有效量子描述的有效性。我们的方法为实现高维玻色-爱因斯坦凝聚体的拓扑规范理论奠定了基础。
