Anyons in an exactly solved model and beyond
Anyons in an exactly solved model and beyond
复制标题
DOI：
10.1016/j.aop.2005.10.005
复制
发表时间：
2006-01-01
影响因子：
3
通讯作者：
Kitaev, A
中科院分区：
文献类型：
--
作者：
Kitaev, A
研究了蜂窝晶格上自旋为1/2的系统。最近邻之间的交互是XX、YY或ZZ类型的，这取决于链接的方向;不同类型的交互的强度可能不同。该模型通过在静态Z（2）规范场中约化为自由费米子而精确求解。在参数空间中的相图。其中一个相位具有能隙，并携带阿贝尔任意子的激发。另一相是无间隙的，但在磁场存在下获得间隙。在后一种情况下，激发是非阿贝尔任意子，其编织规则与伊辛模型的共形块的编织规则一致。我们还考虑了一般理论的自由费米子与一个缺口的频谱，这是其特征在于一个频谱陈数nu。原始模型的阿贝尔相位和非阿贝尔相位分别对应于nu = 0和nu = L。激发的anyonic属性取决于nu mod 16，而nu本身支配边缘热输运。本文还提供了任意子的数学背景以及拟对角矩阵的陈数的基本理论。(c)2005年爱思唯尔公司All rights reserved.
A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z(2) gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number nu. The Abelian and non-Abelian phases of the original model correspond to nu = 0 and nu = L respectively. The anyonic properties of excitation depend on nu mod 16, whereas nu itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices. (c) 2005 Elsevier Inc. All rights reserved.