Zhang G, Li C, Song Z
College of Physics and Materials Science, Tianjin Normal University, Tianjin, 300387, China.
School of Physics, Nankai University, Tianjin, 300071, China.
Sci Rep. 2017 Aug 15;7(1):8176. doi: 10.1038/s41598-017-08323-0.
Mapping a many-body state on a loop in parameter space is a simple way to characterize a quantum state. The connections of such a geometrical representation to the concepts of Chern number and Majorana zero mode are investigated based on a generalized quantum spin system with short and long-range interactions. We show that the topological invariants, the Chern numbers of corresponding Bloch band, is equivalent to the winding number in the auxiliary plane, which can be utilized to characterize the phase diagram. We introduce the concept of Majorana charge, the magnitude of which is defined by the distribution of Majorana fermion probability in zero-mode states, and the sign is defined by the type of Majorana fermion. By direct calculations of the Majorana modes we analytically and numerically verify that the Majorana charge is equal to Chern numbers and winding numbers.
在参数空间的一个环上映射多体状态是表征量子态的一种简单方法。基于具有短程和长程相互作用的广义量子自旋系统，研究了这种几何表示与陈数和马约拉纳零模概念之间的联系。我们表明，拓扑不变量，即相应布洛赫能带的陈数，等同于辅助平面中的缠绕数，可用于表征相图。我们引入马约拉纳电荷的概念，其大小由马约拉纳费米子概率在零模状态下的分布定义，符号由马约拉纳费米子的类型定义。通过对马约拉纳模的直接计算，我们通过解析和数值验证了马约拉纳电荷等于陈数和缠绕数。
