论文标题
矩阵产品状态和预测的纠缠对状态：概念，对称性和定理
Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
论文作者
论文摘要
纠缠理论为描述许多身体系统中的相互作用和相关性提供了一种新的语言。它的词汇由量子和纠缠对组成，语法由张量网络提供。我们回顾了矩阵产品状态和预计的纠缠对态如何用局部张量来描述多体波形。这些张量表达了如何将纠缠的方式路由，充当一种新型的非本地阶参数的类型，我们描述了它们的对称性是对完整系统中全球纠缠模式的反映。我们将讨论张量网络如何启用实际空间重新归一化组和固定点的构建，并检查表现出拓扑量子顺序的状态的纠缠结构。最后，我们提供了矩阵乘积状态和预计纠缠状态的数学结果的摘要，强调了矩阵乘积向量及其应用的基本定理。
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We review how matrix product states and projected entangled pair states describe many-body wavefunctions in terms of local tensors. These tensors express how the entanglement is routed, act as a novel type of non-local order parameter, and we describe how their symmetries are reflections of the global entanglement patterns in the full system. We will discuss how tensor networks enable the construction of real-space renormalization group flows and fixed points, and examine the entanglement structure of states exhibiting topological quantum order. Finally, we provide a summary of the mathematical results of matrix product states and projected entangled pair states, highlighting the fundamental theorem of matrix product vectors and its applications.
