LASSP, Department of Physics, Cornell University, Ithaca, New York 14853, USA.
LASSP, Department of Physics, Cornell University, Ithaca, New York 14853, USA and Department of Physics, Yale University, New Haven, Connecticut 06520, USA.
Phys Rev Lett. 2013 Dec 13;111(24):245701. doi: 10.1103/PhysRevLett.111.245701. Epub 2013 Dec 11.
We present Monte Carlo simulations on a new class of lattice models in which the degrees of freedom are elements of an Abelian or non-Abelian finite symmetry group G, placed on directed edges of a two-dimensional lattice. The plaquette group product is constrained to be the group identity. In contrast to discrete gauge models (but similar to past work on height models), only elements of symmetry-related subsets S∈G are allowed on edges. These models have topological sectors labeled by group products along topologically nontrivial loops. Measurement of relative sector probabilities and the distribution of distance between defect pairs are done to characterize the types of order (topological or quasi-long-range order) exhibited by these models. We present particular models in which fully local non-Abelian constraints lead to global topological liquid properties.
我们提出了一类新的格点模型的蒙特卡罗模拟，其中自由度是阿贝尔或非阿贝尔有限对称群 G 的元素，放置在二维格点的有向边上。 plaquette 群积被约束为群单位元。与离散规范模型（但类似于过去关于高度模型的工作）不同，只有对称相关子集 S∈G 的元素被允许在边上。这些模型具有由拓扑非平凡环路上的群乘积标记的拓扑扇区。通过测量相对扇区概率和缺陷对之间距离的分布来表征这些模型表现出的类型的有序性（拓扑或准长程有序）。我们提出了一些特殊的模型，其中完全局部的非阿贝尔约束导致全局拓扑液体性质。
