Majorana模和边缘态的玻色化
Bosonization of Majorana modes and edge states
摘要：
我们提出了一个玻色化过程，取代费米子与广义自旋变量受局部约束。它要求每个格点的马约拉纳模式的数量与配位数模2相匹配。如果不遵守这个条件，玻色化就会引入原始模型中不存在的额外的费米子激发。在蜂窝晶格上的每个站点的一个马约拉纳模式的情况下，我们恢复一个部门的Kitaev的模型。我们还讨论了十次和矩形几何和目前的玻色化的哈伯德模型。对于有边界的几何，我们发现某些费米边缘模自然出现。它们的性质与物质拓扑相中遇到的边缘模式不同。在我们的建设中产生的类型的自旋系统的无约束版本的欧几里得表示推导和简要研究计算一些精确的平均值小体积。
英文摘要：
We present a bosonization procedure which replaces fermions with generalized spin variables subject to local constraints. It requires that the number of Majorana modes per lattice site matches the coordination number modulo two. If this condition is not obeyed, then bosonization introduces additional fermionic excitations not present in the original model. In the case of one Majorana mode per site on a honeycomb lattice, we recover a sector of Kitaev's model. We discuss also decagonal and rectangular geometries and present bosonization of the Hubbard model. For geometries with a boundary we find that certain fermionic edge modes naturally emerge. They are of different nature than edge modes encountered in topological phases of matter. Euclidean representation for the unconstrained version of a spin system of the type arising in our construction is derived and briefly studied by computing some exact averages for small volumes.
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