论文标题
集体拓扑保护的Majorana fermion fermion激发局部模式网络的激发
Theory of collective topologically-protected Majorana fermion excitations of networks of localized Majorana modes
论文作者
论文摘要
对本地化主要模式的预测以及操纵这些自由度的想法，是针对Majorana量子计算物理平台提案的两个关键要素。几项建议设想通过量子力混合振幅彼此耦合的这种主要模式的可扩展网络。在这里，我们开发了一个理论框架，用于表征这种本地化主要模式网络的集体拓扑保护零能量的零能量激发。 A key ingredient in our work is the Gallai-Edmonds decomposition of a general graph, which we use to obtain an alternate ``local'' proof of a ``global'' result of Lov{á}sz and Anderson on the dimension of the topologically protected null space of {\em real skew-symmetric} (or pure-imaginary hermitean) adjacency matrices of general graphs.我们对Lov {Á} SZ和Anderson的结果的方法为图表的加莱 - 埃德蒙兹分解的上述空空间构建了最大定位的基础。应用于所讨论的Majorana网络的图，这提供了一种表征这些集体拓扑保护的Majorana fermion激励的基础独立属性，并将这些属性与相应网络图的最大匹配（最大包装二聚体盖盖）集合中的单体相关函数联系起来。我们的方法还可以用来识别由自由屈光度汉密尔顿（Hamiltonian）建模的系统中零能量激发的特征，并以这种类型的跳跃矩阵。空缺引起的库里尾巴在基塔耶蜂窝模型的概括（非双色晶格）中提供了一个有趣的例子。
Predictions of localized Majorana modes, and ideas for manipulating these degrees of freedom, are the two key ingredients in proposals for physical platforms for Majorana quantum computation. Several proposals envisage a scalable network of such Majorana modes coupled bilinearly to each other by quantum-mechanical mixing amplitudes. Here, we develop a theoretical framework for characterizing collective topologically protected zero-energy Majorana fermion excitations of such networks of localized Majorana modes. A key ingredient in our work is the Gallai-Edmonds decomposition of a general graph, which we use to obtain an alternate ``local'' proof of a ``global'' result of Lov{á}sz and Anderson on the dimension of the topologically protected null space of {\em real skew-symmetric} (or pure-imaginary hermitean) adjacency matrices of general graphs. Our approach to Lov{á}sz and Anderson's result constructs a maximally-localized basis for the said null-space from the Gallai-Edmonds decomposition of the graph. Applied to the graph of the Majorana network in question, this gives a method for characterizing basis-independent properties of these collective topologically protected Majorana fermion excitations, and relating these properties to the correlation function of monomers in the ensemble of maximum matchings (maximally-packed dimer covers) of the corresponding network graph. Our approach can also be used to identify signatures of zero-energy excitations in systems modeled by a free-fermion Hamiltonian with a hopping matrix of this type; an interesting example is provided by vacancy-induced Curie tails in generalizations (on non-bipartite lattices) of Kitaev's honeycomb model.
