Institutional Repository
| ground-state spaces of frustration-free hamiltonians | |
| Chen Jianxin; Ji Zhengfeng; Kribs David; Wei Zhaohui; Zeng Bei | |
| 2012 | |
| Source | JOURNAL OF MATHEMATICAL PHYSICS
 |
| ISSN | 0022-2488 |
| Volume | 53Issue:10Pages:- |
| English Abstract | We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of "reduced spaces" to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set Theta(k) of all the k-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in Theta(k), called atoms, are analogs of extreme points. We study the properties of atoms in Theta(k) and discuss its relationship with ground states of k-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in Theta(2) are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in Theta(k) may not be the join of atoms, indicating a richer structure for Theta(k) beyond the convex structure. Our study of Theta(k) deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from the new perspective of reduced spaces. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4748527; We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of "reduced spaces" to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set Theta(k) of all the k-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in Theta(k), called atoms, are analogs of extreme points. We study the properties of atoms in Theta(k) and discuss its relationship with ground states of k-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in Theta(2) are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in Theta(k) may not be the join of atoms, indicating a richer structure for Theta(k) beyond the convex structure. Our study of Theta(k) deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from the new perspective of reduced spaces. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4748527 |
| Indexed Type | SCI |
| Department | Chen Jianxin; Kribs David; Zeng Bei Univ Guelph Dept Math & Stat Guelph ON N1G 2W1 Canada. Chen Jianxin; Ji Zhengfeng; Kribs David; Zeng Bei Univ Waterloo Inst Quantum Comp Waterloo ON N2L 3G1 Canada. Ji Zhengfeng Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing Peoples R China. Wei Zhaohui Natl Univ Singapore Ctr Quantum Technol Singapore 117548 Singapore. |
| Subject | Physics |
| Sponsorship | Natural Sciences and Engineering Research Council (Canada) (NSERC); National Science Foundation (NSF) of China 61179030; NSERC 400160, 400233, 400500; U.S. Army Research Office (ARO); Ontario Early Researcher Award 048142; Centre for Quantum Technologies; WBS R-710-000-008-271, R-710-000-007-271; Canadian Institute for Advanced Research (CIFAR) |
| Language | 英语 |
| WOS ID | WOS:000311711000014 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/15061 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Chen Jianxin,Ji Zhengfeng,Kribs David,et al. ground-state spaces of frustration-free hamiltonians[J]. JOURNAL OF MATHEMATICAL PHYSICS,2012,53(10):-. |
| APA | Chen Jianxin,Ji Zhengfeng,Kribs David,Wei Zhaohui,&Zeng Bei.(2012).ground-state spaces of frustration-free hamiltonians.JOURNAL OF MATHEMATICAL PHYSICS,53(10),-. |
| MLA | Chen Jianxin,et al."ground-state spaces of frustration-free hamiltonians".JOURNAL OF MATHEMATICAL PHYSICS 53.10(2012):-. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment