论文标题
保形希尔伯特空间的几何波动和分数量子厅效应中的多个重力模式
Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
论文作者
论文摘要
分数量子厅（FQH）流体中的中性激发定义了拓扑阶段的不可压缩性，拓扑阶段的不可压缩性可以显示出类似引力的行为，因此称为Graviton模式（GMS）。在这里，我们开发了FQH流体中多个GM的显微镜理论，并明确表明它们与定义明确的保形希尔伯特空间（CHS）的几何波动有关，它们在单个Landau级别内是单个Landau级别内的层次子空间，每个子空间都与紧张的形式对称性对称性和持续的参数化。这导致了有关GMS数字和合并/分裂的几个陈述，这些语句通过模型和现实的交互对数字进行了验证。我们还讨论了微观理论如何作为有效现场理论描述中其他HALDANE模式的基础及其与现实的电子电子相互作用的实验相关性。
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.
