论文标题
量子厅状态的自旋统计关系
Spin-statistics relation for quantum Hall states
论文作者
论文摘要
我们证明了出现在磁盘上的阿贝尔量子大厅状态下的分数准颗粒的通用自旋统计关系。该证明是基于一种有效的方法来计算沿圆形路径中平面中翻译成平面中的通用准颗粒获得的浆果相，并且至关重要的事实是，一旦将旋转的量规范发电机投射到landau级别上，它就会在Quasiparticles and Edge之间进行分数化。使用这些结果，我们定义了满足自旋统计关系的可测量的准粒子分数自旋。作为一种应用，我们预测了Jain提出的复合 - fermion Quasielectron的自旋的值；我们的数值模拟同意该值。我们还表明，Laughlin的Quasielectrons满足了旋转统计的关系，但错误的旋转是Laughlin Quasiholes的反对派。我们继续强调一个事实，即可以通过测量角动量在合并两个准粒子的同时测量两个准颗粒之间的统计角。最后，我们表明我们的论点通过明确讨论摩尔阅读波函数来延续到非亚伯案。
We prove a generic spin-statistics relation for the fractional quasiparticles that appear in abelian quantum Hall states on the disk. The proof is based on an efficient way for computing the Berry phase acquired by a generic quasiparticle translated in the plane along a circular path, and on the crucial fact that once the gauge-invariant generator of rotations is projected onto a Landau level, it fractionalizes among the quasiparticles and the edge. Using these results we define a measurable quasiparticle fractional spin that satisfies the spin-statistics relation. As an application, we predict the value of the spin of the composite-fermion quasielectron proposed by Jain; our numerical simulations agree with that value. We also show that Laughlin's quasielectrons satisfy the spin-statistics relation, but carry the wrong spin to be the anti-anyons of Laughlin's quasiholes. We continue by highlighting the fact that the statistical angle between two quasiparticles can be obtained by measuring the angular momentum whilst merging the two quasiparticles. Finally, we show that our arguments carry over to the non-abelian case by discussing explicitly the Moore-Read wavefunction.
