论文标题
系统构造的非液态状态
A systematic construction of gapped non-liquid states
论文作者
论文摘要
间隙非液态状态（也称为Fracton态）是一种非常特殊的量子状态，其特征是微观细胞结构。这种微观细胞结构在任意长距离时具有宏观效应，无法通过重新归一化的组流量消除，这使得与拓扑量子场理论的描述超出了有限数量的磁场。我们在二维（2D）空间中使用Abelian和非阿贝尔拓扑秩序，以及通过其间隙边界将它们粘合在一起的不同方式，我们提出了一种系统的方式来构建3D宽度状态（以及其他维度）。所得状态称为细胞拓扑状态，在某些特殊情况下，其中包括空白的非液态状态以及散发液态。即使使用2D $ \ MATHBB {Z} _2 $拓扑顺序，也构建了一些具有分形激发的新fracton状态。可以通过在不同的3D拓扑顺序之间连接2D域壁来构建更一般的细胞拓扑状态。可以将构造的细胞拓扑状态视为固定点状态，以逆转非液体状态的反向重新归一化。
Gapped non-liquid state (also known as fracton state) is a very special gapped quantum state of matter that is characterized by a microscopic cellular structure. Such microscopic cellular structure has a macroscopic effect at arbitrary long distances and cannot be removed by renormalization group flow, which makes gapped non-liquid state beyond the description of topological quantum field theory with a finite number of fields. Using Abelian and non-Abelian topological orders in 2-dimensional (2d) space and the different ways to glue them together via their gapped boundaries, we propose a systematic way to construct 3d gapped states (and in other dimensions). The resulting states are called cellular topological states, which include gapped non-liquid states, as well as gapped liquid states in some special cases. Some new fracton states with fractal excitations are constructed even using 2d $\mathbb{Z}_2$ topological order. More general cellular topological states can be constructed by connecting 2d domain walls between different 3d topological orders. The constructed cellular topological states can be viewed as fixed-point states for a reverse renormalization of gapped non-liquid states.
