二维拓扑相位、对偶性及三维状态和的微观描述
Microscopic description of 2d topological phases, duality and 3d state sums
摘要：
Kitaev，Levin和Wen在二维格点上引入的双拓扑相是Turaev-Viro态和模型描述的三维拓扑量子场论的哈密顿形式。我们介绍后者，重点是从连续统中的理论中获得它们。利用格点规范理论的群代数和自旋网络基之间的对偶变换，证明了在蜂窝格点和规范群为有限群的情况下，基态模型与已有模型的等价性.分析了这两种模型中描述激励的带状算子和三维几何解释。
英文摘要：
Doubled topological phases introduced by Kitaev, Levin and Wen supported on two dimensional lattices are Hamiltonian versions of three dimensional topological quantum field theories described by the Turaev-Viro state sum models. We introduce the latter with an emphasis on obtaining them from theories in the continuum. Equivalence of the previous models in the ground state are shown in case of the honeycomb lattice and the gauge group being a finite group by means of the well-known duality transformation between the group algebra and the spin network basis of lattice gauge theory. An analysis of the ribbon operators describing excitations in both types of models and the three dimensional geometrical interpretation are given.
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