模矩阵的剪切格度量
Measuring Modular Matrices by Shearing Lattices
摘要：
环面上的拓扑有序相具有简并基态，其在由Dehn扭曲产生的环面的模变换下进行非平凡变换。在基态（模矩阵）上模变换的表示表征了拓扑序。我们表明，模块化矩阵可以数值测量的非阿贝尔Berry相位的绝热变形的晶格模型放置在一个环面。我们将这种方法应用于规范$p_x+i p_y$超导体的例子，并表明其结果与拓扑量子场论的描述是一致的。
英文摘要：
A topologically ordered phase on a torus possesses degenerate ground states that transform nontrivially under the modular transformations of the torus, generated by Dehn twists. Representation of modular transformations on the ground states (modular matrices) characterizes the topological order. We show that the modular matrices can be numerically measured as the non-Abelian Berry phase of adiabatic deformations of the lattice model placed on a torus. We apply this method to the example of a gauged $p_x+i p_y$ superconductor, and show that the result is consistent with the topological quantum field theory descriptions.
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