论文标题
支持纠缠的对称订单
Entanglement-enabled symmetry-breaking orders
论文作者
论文摘要
通常通过一些几个体簇的张量产波功能来描述自发的对称性阶。我们讨论一种对称性的订单，称为纠缠纠缠的对称性订单，任何张量产品状态都无法实现。给定对称性破坏模式，我们提出了一个标准来诊断是否启用了对称性的断裂顺序，通过检查对称性和张量产品描述之间的兼容性。为了具体，我们在与最近的邻居相互作用的一维晶格上呈现一个无限可解决的模型的家族，其基础状态表现出来自离散对称性破坏的纠缠式对称性的破坏订单。此外，这些接地状态具有受不间断对称性保护的无间隙边缘模式。我们还提出了一种结构，以实现具有自发损坏的连续对称性的纠缠对称性命令。在不间断的对称性下，我们的某些例子可以看作是超出传统分类的对称性保护拓扑状态。
A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.
