Systematic construction of gapped nonliquid states
Systematic construction of gapped nonliquid states
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DOI：
10.1103/physrevresearch.2.033300
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发表时间：
2020-02
影响因子：
4.2
通讯作者：
X. Wen
中科院分区：
文献类型：
--
作者：
X. Wen
有隙非液态态(又称分形态)是物质的一种非常特殊的带隙量子态，其特征是具有微观的元胞结构。这种微观晶胞结构在任意长距离具有宏观效应，不能被重整化群流消除，这使得有隙的非液态场超出了有限场数的拓扑量子场论的描述。利用二维空间中的阿贝尔拓扑序和非阿贝尔拓扑序，以及通过它们的缝隙边界将它们粘合在一起的不同方法，我们提出了一种系统的方法来构造3D带隙状态(以及在其他维度中)。由此产生的状态被称为元胞拓扑态，它包括有间隙的非液体状态，以及在某些特殊情况下的有间隙的液体状态。利用2维{Z}2$拓扑序，构造了一些新的具有分形激发的分形态。通过在不同的三维拓扑级之间连接二维畴壁，可以构造出更一般的细胞拓扑态。所构造的元胞拓扑态可以看作是有隙非液态逆重整化的不动点态。
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.