论文标题
分数量子霍尔的旋转统计关系和Abelian编织阶段
Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect
论文作者
论文摘要
分数量子大厅（FQH）系统中的quasihole激发表现出分数统计和分数自旋，但是从多体物理学出现的自旋统计关系如何仍然知之甚少。在这里，我们证明了仅在球体和磁盘几何形状上使用FQH波函数的自旋统计关系。特别是，磁盘上的证据概括为具有有限大小的现实系统中的所有准霍尔斯，并且可以变形为任意形状。 Quasihole旋转的不同组成部分与不同的综合希尔伯特空间（CHS）相关，这些空间是模型的汉密尔顿模型的无孔，它们具有相应的FQH地面状态和Quasihole态。了解准霍尔斯的固有自旋与不同的CHS有关，这对于考虑到度量变形的效果的广义自旋统计关系至关重要。在实验相关性方面，这使我们能够研究浆果曲率的额外来源的变形和混乱的效果，浆果曲率的附加来源，这在以前的文献中很大程度上被忽略了。
Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics relation using only FQH wave functions, on both the sphere and disk geometry. In particular, the proof on the disk generalizes to all quasiholes in realistic systems, which have a finite size and could be deformed into arbitrary shapes. Different components of the quasihole spins are linked to different conformal Hilbert spaces (CHS), which are nullspaces of model Hamiltonians that host the respective FQH ground states and quasihole states. Understanding how the intrinsic spin of the quasiholes is linked to different CHS is crucial for the generalized spin-statistics relation that takes into account the effect of metric deformation. In terms of the experimental relevance, this enables us to study the effect of deformation and disorder that introduces an additional source of Berry curvature, an aspect of anyon braiding that has been largely neglected in previous literature.
