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Title:
Geometry of reduced density matrices for symmetry-protected topological phases
Author: Chen, JY ; Ji, ZF ; Liu, ZX ; Shen, Y ; Zeng, B
Source: PHYSICAL REVIEW A
Issued Date: 2016
Volume: 93, Issue:1
Indexed Type: SCI
Department: 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.
Abstract: 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.
English Abstract: 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.
Language: 英语
WOS ID: WOS:000367659500005
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/17414
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Chen, JY,Ji, ZF,Liu, ZX,et al. Geometry of reduced density matrices for symmetry-protected topological phases[J]. PHYSICAL REVIEW A,2016-01-01,93(1).
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