论文标题
在扭曲的模棱两可的差异（TED）K理论中的任何拓扑顺序
Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
论文作者
论文摘要
虽然通过e二氮理论对非相互作用的晶体拓扑绝缘体阶段进行分类已被广泛接受，但其对任何辅助相互作用阶段的概括 - 因此，对具有拓扑结构的基态的阶段，支持拓扑编织的量子量子 - 仍然敞开。相反，K理论通过分类非相互作用阶段的成功似乎被视为排除了相互作用拓扑顺序的K理论分类。相反，已经探索了其他建议的混合。但是，只有K理论与价电子的实际物理密切相关。自符合性要求任何其他提案都必须与K理论联系起来。 在这里，我们提供了一个详细的论据，以通过扭曲的eproivariant差异（TED）k理论在晶体的brillouin brillouin torus orbi-i-orbi-orbi-orbi-orbi-orbi-orbi-orbienientiford中，通过扭曲的eproivariant差速器（TED）k理论分类对称对称性受保护/增强的su（2） - 孔（2） - 均匀拓扑顺序，尤其是在相互作用的2D半米。 我们尤其认为：（1）拓扑2D半金属阶段Modulo全球质量项由NODAL点补体的平坦差分扭曲的模糊K理论进行了分类； （2）N-电子相互作用阶段通过Brillouin torus中N点的配置空间的K理论进行了分类； （3）“内部局部系统”对epoiriant K理论的扭曲有些被忽视，反映了Chen，Wilczeck，Witten＆Halperin（1989）的有效“虚拟”量规相互作用，该量子将费米斯转化为任何Quanta； （4）诱导的SU（2） - 孔拓扑顺序反映在配置空间上相互作用价束的扭曲的Chern类中，构成了单型辫子表示的超几何积分构建。
While the classification of non-interacting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases -- hence to phases with topologically ordered ground states supporting topological braid quantum gates -- has remained wide open. On the contrary, the success of K-theory with classifying non-interacting phases seems to have tacitly been perceived as precluding a K-theoretic classification of interacting topological order; and instead a mix of other proposals has been explored. However, only K-theory connects closely to the actual physics of valence electrons; and self-consistency demands that any other proposal must connect to K-theory. Here we provide a detailed argument for the classification of symmetry protected/enhanced su(2)-anyonic topological order, specifically in interacting 2d semi-metals, by the twisted equivariant differential (TED) K-theory of configuration spaces of points in the complement of nodal points inside the crystal's Brillouin torus orbi-orientifold. We argue, in particular, that: (1) topological 2d semi-metal phases modulo global mass terms are classified by the flat differential twisted equivariant K-theory of the complement of the nodal points; (2) n-electron interacting phases are classified by the K-theory of configuration spaces of n points in the Brillouin torus; (3) the somewhat neglected twisting of equivariant K-theory by "inner local systems" reflects the effective "fictitious" gauge interaction of Chen, Wilczeck, Witten & Halperin (1989), which turns fermions into anyonic quanta; (4) the induced su(2)-anyonic topological order is reflected in the twisted Chern classes of the interacting valence bundle over configuration space, constituting the hypergeometric integral construction of monodromy braid representations.
