Geometry of reduced density matrices for symmetry-protected topological phases

ISCAS OpenIR

	Geometry of reduced density matrices for symmetry-protected topological phases
	Chen, JY; Ji, ZF; Liu, ZX; Shen, Y; Zeng, B
	2016
发表期刊	PHYSICAL REVIEW A
ISSN	1050-2947
卷号	93 期号:1
摘要	In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low-dimensional projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system-no ruled surface emerges in systems without a boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit where the ground-state degeneracy is exact, we analyze the precision of our numerical algorithm and show that a finite-system calculation suffices to reveal the ruled surface structures.; In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low-dimensional projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system-no ruled surface emerges in systems without a boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit where the ground-state degeneracy is exact, we analyze the precision of our numerical algorithm and show that a finite-system calculation suffices to reveal the ruled surface structures.
收录类别	SCI
部门归属	Tsinghua Univ, Dept Phys, State Key Lab Low Dimens Quantum Phys, Beijing 100084, Peoples R China. Perimeter Inst Theoret Phys, Waterloo, ON, Canada. Univ Waterloo, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada. Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing, Peoples R China. Tsinghua Univ, Inst Adv Study, Beijing 100084, Peoples R China. Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada. Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada.
语种	英语
WOS记录号	WOS:000367659500005
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/17414
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Chen, JY,Ji, ZF,Liu, ZX,et al. Geometry of reduced density matrices for symmetry-protected topological phases[J]. PHYSICAL REVIEW A,2016,93(1).
APA	Chen, JY,Ji, ZF,Liu, ZX,Shen, Y,&Zeng, B.(2016).Geometry of reduced density matrices for symmetry-protected topological phases.PHYSICAL REVIEW A,93(1).
MLA	Chen, JY,et al."Geometry of reduced density matrices for symmetry-protected topological phases".PHYSICAL REVIEW A 93.1(2016).