String and membrane condensation on three-dimensional lattices
String and membrane condensation on three-dimensional lattices
复制标题
三维晶格上的弦和膜凝聚
DOI：
10.1103/physrevb.72.035307
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发表时间：
2004
影响因子：
3.7
通讯作者：
X. Wen
中科院分区：
文献类型：
--
作者：
A. Hamma;P. Zanardi;X. Wen
在本文中，我们研究了具有弦和/或膜缩合基态的Latt Ice自旋模型的一般特性。我们讨论定义字符串或膜操作员所需的属性。我们研究了三个3D自旋模型，这些模型导致低能量下的Z2仪理论。这三个模型都是完全可溶的，并产生了拓扑排序的基态。第一种模式L包含闭合和闭合膜冷凝物。第二个模型仅包含封闭式凝结。开弦的末端表现得像费米子颗粒。第三个模型还具有闭合膜和封闭串的冷凝。开放串的末端是骨器，而开放膜的边缘是费米子的。第三个模型包含一种新型的拓扑顺序。 PACS编号：11.15.-Q，71.10.-W
In this paper, we investigate the general properties of latt ice spin models that have string and/or membrane condensed ground states. We discuss the properties needed to define a string or membrane operator. We study three 3D spin models which lead to Z2 gauge theory at low energies. All the three models are exactly soluble and produce topologically ordered ground states. The first mode l contains both closed-string and closed-membrane condensations. The second model contains closed-string condensation only. The ends of open-strings behave like fermionic particles. The third model also has condensations of closed membranes and closed strings. The ends of open strings are bosonic while the edges of open membranes are fermionic. The third model contains a new type of topological order. PACS numbers: 11.15.-q,71.10.-w