论文标题
高阶纠缠和多体不变式的高阶拓扑阶段
Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
论文作者
论文摘要
我们讨论如何从纠缠的角度来表征强烈相互作用的高阶对称性受保护的拓扑（HOSPT）阶段：首先，我们引入了拓扑多体不变式，该拓扑多体不变性揭示了磁通算子和$ c_n $旋转之间的非交换代数。我们认为，这种不变的表示Instanton携带的角动量与离散的WEN-ZEE响应和分数角电荷密切相关。其次，我们定义了一种称为“高阶纠缠”的新纠缠特性，以仔细检查和区分各种高阶拓扑阶段与纠缠结构的分层序列。我们通过数字研究表现出不同HOSPT阶段的超级晶格玻色纸模型来支持我们的主张。
We discuss how strongly interacting higher-order symmetry protected topological (HOSPT) phases can be characterized from the entanglement perspective: First, we introduce a topological many-body invariant which reveals the non-commutative algebra between flux operator and $C_n$ rotations. We argue that this invariant denotes the angular momentum carried by the instanton which is closely related to the discrete Wen-Zee response and fractional corner charge. Second, we define a new entanglement property, dubbed `higher-order entanglement', to scrutinize and differentiate various higher-order topological phases from a hierarchical sequence of the entanglement structure. We support our claims by numerically studying a super-lattice Bose-Hubbard model that exhibits different HOSPT phases.
