论文标题
二元性观点
Duality viewpoint of criticality
论文作者
论文摘要
在这项工作中，我们研究了在二元转换下是自二的量子多体系统，该系统连接了不同的对称性受保护的拓扑（SPT）阶段。我们提供了这些自动划分模型的批判性的几何解释。更确切地说，我们在周期性边界条件下（即块状频谱的不合同性）显示了基态（准）退化。同等地，包括二元对称性在内的临界性对称组具有混合的异常现象。这种方法不仅可以通过普通0形式对称性来预测自偶联模型的频谱，而且还可以用广义对称性（例如较高的形式和子系统对称性）应用于这种模型。作为一个应用程序，我们用一个和二维的几个示例说明了结果，它们将两个不同的SPT分开。
In this work, we study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological (SPT) phases. We provide a geometric explanation of the criticality of these self-dual models. More precisely, we show a ground state (quasi-)degeneracy under the periodic boundary conditions,i.e., the ingappability of the bulk spectrum. Equivalently, the symmetry group at criticality, including the duality symmetry, has a mixed 't Hooft anomaly. This approach can not only predict the spectrum of the self-dual model with ordinary 0-form symmetry, but also be applied to that with generalized symmetry, such as higher form and subsystem symmetry. As an application, we illustrate our results with several examples in one and two dimensions, which separate two different SPTs.
