Dynamical Gauge Fields and Fractional Chern Insulators

动态规范场和分数陈绝缘体

• 批准号: 430670757
• 负责人: Professor Dr. Fabian Grusdt
• 金额: --
• 依托单位: Arnold Sommerfeld Center for Theoretical Physics
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/430670757?language=en
• 关键词: Dynamical; Gauge; Fields; Fractional; Chern

We investigate strongly interacting states of quantum matter interacting with dynamical gauge fields. One part of the project focuses on fractional Chern insulators, in which dynamical gauge fields can lead to flux-attachment and to the formation of weakly interacting composite fermions. The second part of the project is concerned with the simplest instant of a lattice gauge theory (LGT) - an Ising or Z2 LGT - coupled to a matter field. Both system are now within reach of ultracold atom experiments in optical lattices, thanks to the capabilities achieved by resonant lattice modulations. Here we will study theoretically various aspects of these models, which allow on one hand to connect to long-standing problems involving strongly correlated electrons and which are of immediate experimental relevance on the other hand. These include (A) the theoretical description of fractional Chern insulators, with special emphasis on the role of lattice effects and the bosonic Pfaffian state at unit magnetic filling hosting non-Abelian excitations; (B) The study of Z2 LGTs coupled to matter fields and their phase diagram in quasi-one dimensional multi-leg ladder geometries; And (C) dynamical probes of such strongly correlated states of matter, with special emphasis on spectroscopic probes of the underlying topological properties. Our main tool will be state-of-the-art DMRG simulations, extended to time-dependent calculations and two-dimensional systems. Additionally, we will perform physically motivated variational calculations.

研究了量子物质与动力学规范场相互作用的强相互作用态。该项目的一部分集中在分数陈绝缘体上，在这种绝缘体中，动态规范场可以导致磁通附着和形成弱相互作用的复合费米子。该项目的第二部分涉及格点规范理论(LGT)的最简单时刻-Ising或Z2 LGT-耦合到物质场。由于共振晶格调制的能力，这两个系统现在都可以在光学晶格中进行超冷原子实验。在这里，我们将从理论上研究这些模型的各个方面，这些模型一方面允许与涉及强关联电子的长期存在的问题相联系，另一方面又具有直接的实验意义。这些包括(A)分数陈氏绝缘体的理论描述，特别强调晶格效应和单位磁填充下的玻色子Pfaffian态在非阿贝尔激发下的作用；(B)Z2 LGT与物质场的耦合及其在准一维多支梯几何中的相图的研究；以及(C)对这种强关联态物质的动力学探测，特别强调潜在的拓扑性质的光谱探测。我们的主要工具将是最先进的DMRG模拟，扩展到与时间相关的计算和二维系统。此外，我们还将执行物理激励的变分计算。