Dynamical Gauge Fields and Fractional Chern Insulators

我们研究了量子物质与动态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氏绝缘体，其中动态规范场可以导致通量附着和弱相互作用复合费米子的形成。该项目的第二部分是关于格点规范理论（LGT）的最简单的瞬间-伊辛或Z2 LGT -耦合到一个物质场。这两个系统现在都可以在光学晶格中进行超冷原子实验，这要归功于共振晶格调制所实现的能力。在这里，我们将从理论上研究这些模型的各个方面，一方面可以连接到长期存在的问题，涉及强相关的电子，这是直接的实验相关的另一方面。其中包括（A）分数Chern绝缘体的理论描述，特别强调晶格效应的作用和非阿贝尔激发下单位磁填充的玻色Pfronian态：（B）准一维多腿梯形几何中耦合到物质场的Z 2 LGT及其相图的研究;以及（C）对这种强关联态物质的动力学探测，特别强调对潜在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，扩展到时间相关的计算和二维系统。此外，我们将执行物理动机的变分计算。

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.