BDI类拓扑超导体的精确可解自旋链模型
Exactly solvable spin chain models corresponding to BDI class of topological superconductors
摘要：
我们提出了一个具有长程多自旋相互作用的量子XY链的精确可解扩展。拓扑相变的模型进行分类的马约拉纳零模式，这反过来又涉及到一个整数绕组数的数量。我们还发现了开链两端的缠绕数和马约拉纳费米子数之间的一般关系。目前这类精确可解模型属于Altland-Zirnbauer分类中的BDI类（A. Altland，M. R. Zirnbauer，Phys. Rev. B（1997）55 1142）。我们表明，时间反演（TR）的自旋变量的对称性转化为一个特殊的粒子-空穴变换的语言乔丹-维格纳（JW）费米子，伴随着一个π位移的波矢量（$π$ PH）。$π$ PH对称性的存在将XY的TR对称扩张的缠绕数限制为奇数。πPH算符可用于拓扑超导体的进一步详细分类。
英文摘要：
We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes which are in turn related to an integer winding number. We further find a general relation between the winding number and the number of Majorana fermions at the ends of an open chain. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification (A. Altland, M. R. Zirnbauer, Phys. Rev. B (1997) 55 1142) of topological superconductors. We show that time reversal (TR) symmetry of the spin variables translates into a peculiar particle-hole transformation in the language of Jordan-Wigner (JW) fermions that is accompanied by a π shift in the wave vector ($π$PH). Presence of $π$PH symmetry restricts the winding number of TR symmetric extensions of XY to odd integers. The πPH operator may serve in further detailed classification of topological superconductors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
