论文标题
斐波那契分数量子霍尔状态的复合粒子结构
A composite particle construction of the Fibonacci fractional quantum Hall state
论文作者
论文摘要
斐波那契拓扑顺序是通用拓扑量子计算机的最简单平台，该平台由单一类型的非亚伯利亚人Anyon，$τ$，其中融合规则$τ\timesτ= 1+τ$。虽然有人提出，$ν= 12/5 $的量子量子厅状态的Anyon光谱包括一个斐波那契扇区，但动态图片表明，在量子厅系统中如何出现纯的斐波那契状态。在这里，我们最近使用拟议的非亚洲二重性来构建玻色子的斐波那契状态，以填充$ν= 2 $，从整数量子霍尔的三层开始。我们的父理论由玻色粒“复合涡旋”组成，并与波动$ u（2）$ gauge字段相结合，这与双重性的Laughlin Quasiparticles的标准理论有关。斐波那契状态是通过将层之间的复合涡流以及磁通附件聚集来获得的。我们进一步使用此框架来激励斐波那契分数量子霍尔状态的波浪函数。
The Fibonacci topological order is the simplest platform for a universal topological quantum computer, consisting of a single type of non-Abelian anyon, $τ$, with fusion rule $τ\timesτ=1+τ$. While it has been proposed that the anyon spectrum of the $ν=12/5$ fractional quantum Hall state includes a Fibonacci sector, a dynamical picture of how a pure Fibonacci state may emerge in a quantum Hall system has been lacking. Here we use recently proposed non-Abelian dualities to construct a Fibonacci state of bosons at filling $ν=2$ starting from a trilayer of integer quantum Hall states. Our parent theory consists of bosonic "composite vortices" coupled to fluctuating $U(2)$ gauge fields, which is related to the standard theory of Laughlin quasiparticles by duality. The Fibonacci state is obtained by clustering the composite vortices between the layers, along with flux attachment, a procedure reminiscent of the clustering picture of the Read-Rezayi states. We further use this framework to motivate a wave function for the Fibonacci fractional quantum Hall state.
