Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons
Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons
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DOI：
10.1103/physrevx.8.021074
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发表时间：
2018-06-22
影响因子：
12.5
通讯作者：
Wen, Xiao-Gang
中科院分区：
文献类型：
--
作者：
Lan, Tian;Kong, Liang;Wen, Xiao-Gang
拓扑序是超越朗道对称性破缺的物质的新相。它们与长程纠缠的模式相对应。近年来的研究表明，在1+1D玻色子系统中，不存在非平凡的拓扑序，而在2+1D玻色子系统中，拓扑序可分为模张量范畴和手征中心电荷对。本文遵循一种新的思路，发现在3+1D中，拓扑序的分类比人们所认为的要简单得多；我们提出了3+1D玻色子系统拓扑序的偏分类：如果所有的点状激发都是玻色子，那么这种拓扑序可以用一个更简单的对(G，omega(4))来分类：有限群G及其群4-余圈omega(4)是H-4[G；U(1)](至群自同构)的一个元素。此外，所有这种3+1维拓扑有序都可以用Dijkgraaf-Witten规范理论来实现。
Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1 + 1D bosonic systems, there is no nontrivial topological order, while in 2 + 1D bosonic systems, the topological orders are classified by the following pair: a modular tensor category and a chiral central charge. In this paper, following a new line of thinking, we find that in 3 + 1D the classification is much simpler than it was thought to be; we propose a partial classification of topological orders for 3 + 1 D bosonic systems: If all the pointlike excitations are bosons, then such topological orders are classified by a simpler pair (G, omega(4)): a finite group G and its group 4-cocycle omega(4) is an element of H-4 [G; U(1)] (up to group automorphisms). Furthermore, all such 3 + 1D topological orders can be realized by Dijkgraaf-Witten gauge theories.