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	Boundary-bulk relation in topological orders
	Kong, Liang ; Wen, Xiao-Gang ; Zheng, Hao
	2017
关键词	QUANTUM COMPUTATION DOMAIN-WALLS ANYONS ALGEBRA PHASES
英文摘要	In this paper, we study the relation between an anomaly-free n+1D topological order, which are often called n+1D topological order in physics literature, and its nD gapped boundary phases. We argue that the n+1D bulk anomaly-free topological order for a given nD gapped boundary phase is unique. This uniqueness defines the notion of the "(bulk) under bar" for a given gapped boundary phase. In this paper, we show that the n+1D "(bulk) under bar" phase is given by the "center" of the nD boundary phase. In other words, the geometric notion of the "(bulk) under bar" corresponds precisely to the algebraic notion of the " center". We achieve this by first introducing the notion of a morphism between two (potentially anomalous) topological orders of the same dimension, then proving that the notion of the "(bulk) under bar" satisfies the same universal property as that of the " center" of an algebra in mathematics, i.e. "(bulk) under bar= center". The entire argument does not require us to know the precise mathematical description of a (potentially anomalous) topological order. This result leads to concrete physical predictions. (C) 2017 The Author(s). Published by Elsevier B.V.; NSF [DMR-1506475]; NSFC [11274192, 11131008]; SCI(E); ARTICLE; 62-76; 922
语种	英语
出处	SCI
出版者	NUCLEAR PHYSICS B
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/471091]
专题	数学科学学院
推荐引用方式 GB/T 7714	Kong, Liang,Wen, Xiao-Gang,Zheng, Hao. Boundary-bulk relation in topological orders. 2017-01-01.

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