Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums
Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums
复制标题
2D 拓扑相、对偶性和 3D 状态和的微观描述
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
M. Rasetti
中科院分区：
文献类型：
--
作者：
Z. Kádár;A. Marzuoli;M. Rasetti
由Kitaev，Levin和Win在二维晶格上引入的双重拓扑相是由Turaev-Viro态和模型描述的三维拓扑量子场理论的哈密顿版本。我们介绍了后者，重点是从连续体的理论中获得它们。在蜂窝晶格和规范群为有限群的情况下，借助于格点规范理论的群代数和自旋网络基之间众所周知的对偶变换，证明了在基态下上述模型的等价性。对两种模型中描述激发的带状算符进行了分析，并给出了三维几何解释。
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 is 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.