Coupled wire model of Z4 orbifold quantum Hall states
Coupled wire model of
Z4
orbifold quantum Hall states
复制标题
Z4轨道量子霍尔态的耦合线模型
DOI：
10.1103/physrevb.98.085302
复制
发表时间：
2018
影响因子：
3.7
通讯作者：
A. Stern
中科院分区：
文献类型：
--
作者：
C. Kane;A. Stern
我们引入了一个非阿贝尔量子霍尔态序列的耦合线模型，推广了Z4 parafermion Read Rezayi态。Z4轨道量子霍尔态发生在填充因子\nu = 2/（2 m-p）的奇数$m$和$p$，并有一个拓扑顺序与中性扇区的特征是轨道共形场论与中心电荷$c=1$在半径$R=\sqrt{p/2}$。当p=1时，状态是阿贝尔的。$p=3$的状态是$Z_4$ Read Rezayi状态，而$p\ge 3$的序列定义了一个类似于Laughlin序列的非阿贝尔状态序列。我们的模型是基于集群的电子在四个组，并制定为两个流体模型，其中每根线表现出两个阶段：一个弱的集群阶段，其中电荷$e$电子共存的电荷$4e$玻色子和一个强的集群阶段，其中的电子强烈绑定在4组。这两个阶段之间的过渡线被映射到临界点的4态时钟模型，这反过来又是描述的轨道共形场理论。对于一个阵列的导线耦合在一个垂直磁场的存在下，强烈聚集的导线形成一个电荷$4e$玻色子劳克林状态的手性电荷模式在边缘，但没有中性模式和单电子的间隙。临界态附近的耦合线形成量子霍尔态，具有轨道理论描述的无隙中性模式。耦合线方法允许我们采用阿贝尔玻色化技术来充分分析单线的物理，然后提取所得到的非阿贝尔量子霍尔态的大多数拓扑性质。这些包括准粒子的列表，它们的融合规则，大块准粒子和边缘拓扑扇区之间的对应关系，以及大多数与准粒子相互缠绕相关的相位。
We introduce a coupled wire model for a sequence of non-Abelian quantum Hall states that generalize the Z4 parafermion Read Rezayi state. The Z4 orbifold quantum Hall states occur at filling factors \nu = 2/(2m-p) for odd integers $m$ and $p$, and have a topological order with a neutral sector characterized by the orbifold conformal field theory with central charge $c=1$ at radius $R=\sqrt{p/2}$. When $p=1$ the state is Abelian. The state with $p=3$ is the $Z_4$ Read Rezayi state, and the series of $p\ge 3$ defines a sequence of non-Abelian states that resembles the Laughlin sequence. Our model is based on clustering of electrons in groups of four, and is formulated as a two fluid model in which each wire exhibits two phases: a weak clustered phase, where charge $e$ electrons coexist with charge $4e$ bosons and a strong clustered phase where the electrons are strongly bound in groups of 4. The transition between these two phases on a wire is mapped to the critical point of the 4 state clock model, which in turn is described by the orbifold conformal field theory. For an array of wires coupled in the presence of a perpendicular magnetic field, strongly clustered wires form a charge $4e$ bosonic Laughlin state with a chiral charge mode at the edge, but no neutral mode and a gap for single electrons. Coupled wires near the critical state form quantum Hall states with a gapless neutral mode described by the orbifold theory. The coupled wire approach allows us to employ the Abelian bosonization technique to fully analyze the physics of single wire, and then to extract most topological properties of the resulting non-Abelian quantum Hall states. These include the list of quasiparticles, their fusion rules, the correspondence between bulk quasiparticles and edge topological sectors, and most of the phases associated with quasiparticles winding one another.