Bogoliubov-de Gennes对角化与Schur分解方法的等价性  

Equivalence between Bogoliubov-de Gennes Diagonalization and Schur Decomposition

作　　者：张雨 黄镇华 李铭[1] 

机构地区：[1]华南师范大学物理与电信工程学院,广东省量子调控与材料重点实验室,广州510006

出　　处：《华南师范大学学报（自然科学版）》2017年第6期12-16,共5页Journal of South China Normal University(Natural Science Edition)

基　　金：广东省教育厅团队项目(C1085031)

摘　　要：以Kitaev的一维量子线模型为例,分别利用传统的Bogoliubov-de Gennes(Bd G)对角化方法和Schur分解方法求解该模型的本征能量以及本征波函数,从理论分析和数值计算方面对2种方法进行对比.结果表明,Bd G对角化方法得到的准粒子能量是能量本征值的2倍,而Schur分解方法可以直接得到准粒子能量.两者数值计算结果一致.另外,在确定的参数下,2种方法得到的准粒子算符对初始的费米子算符的展开系数只相差一个常数相因子.所以,最后的结论是Bd G对角化跟Schur分解两种方法是等价的.The Equivalence between the Bogoliubov-de Gennes( Bd G) Diagonalization method and the Schur decomposition has been verified through numerical computations to the Kitaev model of a one-dimensional quantum wire. Comparisons between two methods have been conducted in terms of theoretical analysis and numerical computation. The quasipartical energies obtained from the Bd G method are twice the eigenenergies but the Schur decomposition gives the quasipartical energies directly. The numerical results show that quasipartical energies from the two methods are consistent with each other perfectly. In addition,the expansion coefficients of the quasipartical operators from two methods have only a constant phase in difference. The final conclusion is drawn that Bd G diagonalization method and Schur decomposition are equivalent.

关 键 词：Bd G对角化方法 SCHUR分解 Majonara费米子 粒子-空穴对称 拓扑绝缘体 

分 类 号：O41[理学—理论物理]