不可区分群中量子组织的非阿贝尔拓扑序
Non-Abelian Topological Order from Quantum Organization in Indistinguishable Groups
摘要：
我提出，非阿贝尔拓扑秩序可以出现从组织的量子粒子到相同的量子多体状态的相同的不可区分的副本。集体的量子不变性（对称化）导致了基本激发子空间的拓扑简并，产生了非阿贝尔编织统计。对称化结构的非阿贝尔隐序表现在其纠缠特性上，通过分析具有非平凡拓扑结构的环面上的对称化态集，可以得到相应的非阿贝尔融合和编织规则.为了说明非阿贝尔统计对称化的出现，我考虑了两个相同的复曲面代码模型的副本的情况。由此产生的模型被证明是非阿贝尔，表现出两种类型（电荷和通量）的准粒子与非平凡的融合通道。我在这里提出的对称化结构构成了一个框架，用于从已知的阿贝尔模型生成非阿贝尔模型。
英文摘要：
I propose that non-Abelian topological order can emerge from the organization of quantum particles into identical indistinguishable copies of the same quantum many-body state. Quantum indistinguishability (symmetrization) of the collectivities leads to topological degeneracy in the subspace of elementary excitations, giving rise to non-Abelian braiding statistics. The non-Abelian hidden order of a symmetrized structure is manifested in its entanglement properties, and the corresponding non-Abelian fusion and braiding rules can be derived by analyzing the set of symmetrized states on a surface with non-trivial topology like a torus. To illustrate the emergence of non-Abelian statistics from symmetrization, I consider the case of two identical copies of the toric code model. The resulting model is shown to be non-Abelian, exhibiting two types (charge and flux) of quasiparticles with non trivial fusion channels. The symmetrization construction I present here constitutes a framework for the generation of non-Abelian models from known Abelian ones.
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