Non-Abelian SU (N-1)-singlet fractional quantum Hall states from coupled wires
Non-Abelian SU (N-1)-singlet fractional quantum Hall states from coupled wires
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来自耦合线的非阿贝尔 SU (N-1)-单线分数量子霍尔态
DOI：
10.1103/physrevb.95.125130
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发表时间：
2016
影响因子：
3.7
通讯作者：
P. Lecheminant
中科院分区：
文献类型：
--
作者：
Y. Fuji;P. Lecheminant
利用二维量子线阵列构造分数量子霍尔态为控制微观模型中的强相互作用提供了一种有用的方法，并已成功地应用于Laughlin态、Moore-Read态和Read-Rezayi态。我们将这种结构推广到填充分数为$\nu=k(N-1)/[N+k(N-1)m]$的阿贝尔和非阿贝尔的$SU(N-1)$-单重态FQH态，这在多组分量子霍尔系统或自旋系统中是有可能实现的。利用玻色化方法和共形场理论(CFT)，我们证明了它们的整体准粒子和无间隙边缘激发都可以用一个$(N-1)$分量自由玻色子CFT和称为Gepner准分子的$SU(N)_k/[U(1)]^{N-1}$CFT来描述。并将它们推广到不同的填充分数。此外，我们还讨论了这些结果在两类晶格系统中的可能应用：玻色子通过占据相关跃迁相互作用和$SU(N)$Heisenberg模型。
The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin, Moore-Read, and Read-Rezayi states. We extend this construction to the Abelian and non-Abelian $SU(N-1)$-singlet FQH states at filling fraction $\nu=k(N-1)/[N+k(N-1)m]$ labeled by integers $k$ and $m$, which are potentially realized in multi-component quantum Hall systems or $SU(N)$ spin systems. Utilizing the bosonization approach and conformal field theory (CFT), we show that their bulk quasiparticles and gapless edge excitations are both described by an $(N-1)$-component free-boson CFT and the $SU(N)_k/[U(1)]^{N-1}$ CFT known as the Gepner parafermion. Their generalization to different filling fractions is also proposed. In addition, we argue possible applications of these results to two kinds of lattice systems: bosons interacting via occupation-dependent correlated hoppings and an $SU(N)$ Heisenberg model.