论文标题
在丰富的复曲面代码中用于对称分数的字符串顺序参数
String order parameters for symmetry fractionalization in an enriched toric code
论文作者
论文摘要
我们研究了一个简单的对称式拓扑秩序的模型，该模型通过以较低的对称性保护拓扑状态来装饰复曲面代码模型获得。我们表明，该模型中的对称分数可以以字符串顺序参数为特征，并且在外部磁场和相互作用的效果下，这些签名是可靠的，直到相变点。这将[新物理学杂志21，113016（2019）]的最新建议延伸到固定点张量网络状态的设置之外，并巩固了字符串顺序参数，作为表征和检测对称分数化的有用工具。除此之外，我们还观察到一个对称力的对称力的凝结是如何自发打破的，并且在投影纠缠的一对状态的框架中给出了这一点。这种现象导致在平行磁场中曲折代码的相图发生了显着变化。
We study a simple model of symmetry-enriched topological order obtained by decorating a toric code model with lower-dimensional symmetry-protected topological states. We show that the symmetry fractionalization in this model can be characterized by string order parameters, and that these signatures are robust under the effects of external fields and interactions, up to the phase transition point. This extends the recent proposal of [New Journal of Physics 21, 113016 (2019)] beyond the setting of fixed-point tensor network states, and solidifies string order parameters as a useful tool to characterize and detect symmetry fractionalization. In addition to this, we observe how the condensation of an anyon that fractionalizes a symmetry forces that symmetry to spontaneously break, and we give a proof of this in the framework of projected entangled pair states. This phenomenon leads to a notable change in the phase diagram of the toric code in parallel magnetic fields.
