论文标题
手性拓扑排序的绝缘阶段在相互作用的整数量子霍尔群岛中
Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
论文作者
论文摘要
我们研究库仑块的整数量子霍尔岛的网络，均匀填充$ν= 2k $（$ k $是整数），其中包括$ 2k $ layers $ n $ν= 1 $填充物的箱子。我们仅允许岛屿之间的自旋 - 电流相互作用（即，没有任何充电转移），我们获得了可解决的模型，导致一组丰富的绝缘$ SU（2）_K $拓扑订购的阶段。 $ k = 1 $的案例对Kalmeyer-Laughlin阶段是双重的，$ k = 2 $ to Kitaev的手性旋转液体和Moore-pread State，$ k = 3 $包含一个可用于通用拓扑量学计算的斐波那契。此外，我们还展示了如何在$ν= 2k $ integer量子厅状态和棋盘格式中的关键旋转链中获得$ su（2）_k $拓扑阶段。阵列和棋盘构建由于其几何形状而散布了充电模式和其他“风味”模式。此外，我们发现Checkboard配置中不需要对系统参数进行微调和$ν= 2 $ case。我们还讨论了他们的大量激发，并表明他们的热厅电导是通用的，反映了手性边缘模式的中央电荷$ c = 3k/（k+2）$。
We study networks of Coulomb-blockaded integer quantum Hall islands with even fillings $ν=2k$ ($k$ being an integer), including cases with $2k$ layers each of $ν=1$ fillings. Allowing only spin-current interactions between the islands (i.e., without any charge transfer), we obtain solvable models leading to a rich set of insulating $SU(2)_k$ topologically ordered phases. The case with $k=1$ is dual to the Kalmeyer-Laughlin phase, $k=2$ to Kitaev's chiral spin liquid and the Moore-Read state, and $k=3$ contains a Fibonacci anyon that may be utilized for universal topological quantum computation. Additionally, we show how the $SU(2)_k$ topological phases may be obtained also in an array of islands with $ν=2k$ integer quantum Hall states and critical spin chains in a checkerboard pattern. The array and checkerboard constructions gap out the charge mode and additional "flavor" modes by virtue of their geometry. Furthermore, we find that a fine tuning of the system parameter is not needed in the checkerboard configuration and the $ν=2$ case. We also discuss their bulk excitations, and show that their thermal Hall conductance is universal, reflecting the central charge $c=3k/(k+2)$ of the chiral edge modes.
