论文标题
拓扑相转换及以后的纠缠顺序参数和关键行为
Entanglement order parameters and critical behavior for topological phase transitions and beyond
论文作者
论文摘要
拓扑阶段是异国情调的量子相，在顺序参数方面缺乏表征。在本文中，我们基于各种IPEP来开发一个统一的框架，以通过纠缠顺序参数对拓扑和常规相变的定量研究。为此，我们采用了编码的适当的物理和/或纠缠对称性的张量网络，并允许订单参数检测任何对称性的物理和纠缠的对称性的行为。首先，这引起了拓扑阶段的基于纠缠的订单参数。这些拓扑顺序参数允许定量探测拓扑相变并确定其普遍行为。我们将我们的框架应用于不同磁场的曲折代码模型的研究，在某些情况下，该模型映射到（2+1）d Ising模型。我们确定了整个过渡的3D关键指数，与这些特殊情况和一般信念一致。但是，我们发现一个未知的关键指数beta = 0.021。然后，我们将纠缠订单参数的框架应用于常规相变。我们构建了一种新型的疾病操作员（或疾病参数），该类型在无序相中并非零，并测量波函数对纠缠中对称性扭曲的响应。我们对（2+1）d横向场ISING模型进行数值评估该疾病操作员，在该模型中，我们再次恢复了迄今未知的关键指数，beta = 0.024，与圆环代码的发现一致。这表明，纠缠顺序参数可以提供在拓扑和常规相变时表征通用数据的其他手段，并且完全证明了该框架的力量以识别过渡基础的通用数据。
Topological phases are exotic quantum phases which are lacking the characterization in terms of order parameters. In this paper, we develop a unified framework based on variational iPEPS for the quantitative study of both topological and conventional phase transitions through entanglement order parameters. To this end, we employ tensor networks with suitable physical and/or entanglement symmetries encoded, and allow for order parameters detecting the behavior of any of those symmetries, both physical and entanglement ones. First, this gives rise to entanglement-based order parameters for topological phases. These topological order parameters allow to quantitatively probe topological phase transitions and to identify their universal behavior. We apply our framework to the study of the Toric Code model in different magnetic fields, which in some cases maps to the (2+1)D Ising model. We identify 3D Ising critical exponents for the entire transition, consistent with those special cases and general belief. However, we moreover find an unknown critical exponent beta=0.021. We then apply our framework of entanglement order parameters to conventional phase transitions. We construct a novel type of disorder operator (or disorder parameter), which is non-zero in the disordered phase and measures the response of the wavefunction to a symmetry twist in the entanglement. We numerically evaluate this disorder operator for the (2+1)D transverse field Ising model, where we again recover a critical exponent hitherto unknown in the model, beta=0.024, consistent with the findings for the Toric Code. This shows that entanglement order parameters can provide additional means of characterizing the universal data both at topological and conventional phase transitions, and altogether demonstrates the power of this framework to identify the universal data underlying the transition.
