School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore.
Institute of High Performance Computing, A*STAR, Singapore, 138632, Singapore.
Nat Commun. 2023 Apr 21;14(1):2317. doi: 10.1038/s41467-023-38036-0.
Neutral excitations in fractional quantum Hall (FQH) fluids define the incompressibility of topological phases, a species of which can show graviton-like behaviors and are thus called the graviton modes (GMs). Here, we develop the microscopic theory for multiple GMs in FQH fluids and show explicitly that they are associated with the geometric fluctuation of well-defined conformal Hilbert spaces (CHSs), which are hierarchical subspaces within a single Landau level, each with emergent conformal symmetry and continuously parameterized by a unimodular metric. This leads to several statements about the number and the merging/splitting of GMs, which are verified numerically with both model and realistic interactions. We also discuss how the microscopic theory can serve as the basis for the additional Haldane modes in the effective field theory description and their experimental relevance to realistic electron-electron interactions.
分数量子霍尔（FQH）流体中的中性激发定义了拓扑相的不可压缩性，其中一种可以表现出类引力子行为，因此被称为引力子模式（GMs）。在这里，我们发展了 FQH 流体中多个 GMs 的微观理论，并明确表明它们与明确定义的共形希尔伯特空间（CHSs）的几何涨落有关，CHSs 是单个朗道能级内的层次子空间，每个子空间都具有涌现的共形对称性，并由单模度量连续参数化。这导致了关于 GMs 的数量及其合并/分裂的几个陈述，这些陈述已经通过模型和实际相互作用进行了数值验证。我们还讨论了微观理论如何成为有效场论描述中额外的 Haldane 模式的基础，以及它们与实际电子-电子相互作用的实验相关性。
