发表机构
Pennsylvania State University; Lodha Theoretical Physics Institute（宾夕法尼亚州立大学; 洛达理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究分数量子霍尔准粒子绕行时的贝里相位，发现其包含面积主导的AB项、形状依赖项和编织项，形状项可掩盖编织统计，并指出干涉实验的分数相位跳变源于体态准粒子的分数涡度。
AI 中文摘要
对于“理想任意子”，一个任意子绕另一个任意子闭合回路的贝里相位是稳健的，即与回路的大小或形状无关，并直接给出编织统计。但对于分数量子霍尔（FQH）准粒子（QPs）而言，情况并非如此，它们带电且具有有限尺寸。我们在此考虑贝里相位如何依赖于准粒子的形状，与电荷不同，形状不是拓扑性质，并沿路径响应局域势而变化。我们证明，一个带分数电荷的准粒子绕另一个准粒子的回路所关联的贝里相位 $\Theta$ 包含三个不同的贡献：$\Theta=\Theta_{\rm AB}+\Theta_{\rm shape}+\Theta_{\rm braid}$。阿哈罗诺夫-玻姆相位 $\Theta_{\rm AB}$ 占主导，正比于回路面积，而本文中确定的形状依赖项 $\Theta_{\rm shape}$ 可能大于来自编织统计的阶数为一的贡献 $\Theta_{\rm braid}$。精确确定编织统计具有挑战性，因为它可能被实际不可检测的轨迹和形状不确定性所淹没。我们在干涉实验的背景下讨论这些结果。我们还注意到，这些实验中的分数相位跳变可以在不假设FQH系统边缘存在具有尖锐量子化分数电荷的准粒子的情况下理解，其中这些相位跳变直接度量了分数量子霍尔态体态中准粒子的分数量子化涡度。
英文摘要
For ``ideal anyons,'' the Berry phase associated with a closed loop of an anyon around another is robust, i.e., independent of the size and shape of the loop, and directly yields the braid statistics. This is not the case for fractional quantum Hall (FQH) quasiparticles (QPs), which are charged and have finite size. The Berry phase $Θ$ associated with a loop of a fractionally charged QP around another contains two contributions: $Θ=Θ_{\rm AB}+Θ_{\rm braid}$, where $Θ_{\rm AB}$, the Aharonov-Bohm phase, is proportional to the enclosed area, and $Θ_{\rm braid}$ is the order-one contribution from braid statistics. The latter is obtained by determining $Θ$ for a closed loop twice, once with and once without the other QP inside, and taking the difference. It is known that even small uncertainties in the enclosed areas can produce corrections to $Θ_{\rm AB}$ larger than $Θ_{\rm braid}$. We consider how the Berry phase depends on the shape of the QP, which, unlike its charge, is not topological and varies along the path in response to the local potential. Our calculations show that practically imperceptible differences in the shape of the outer QP in the two experiments can produce a non-universal value for the braid statistics, revealing an additional challenge for a precise determination of the braid statistics. We discuss these results in the context of interference experiments. We also note that the fractional phase jumps in these experiments can be understood without assuming QPs with sharply quantized fractional charges at the edges of the FQH system; instead, they directly measure the fractionally quantized vorticity of bulk QPs.
Comments53 pages, 27 figures. Comments are welcome. v2: corrected minor grammatical errors
