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| correlations in excited states of local hamiltonians | |
| Chen Jianxin; Ji Zhengfeng; Wei Zhaohui; Zeng Bei | |
| 2012 | |
| Source | Physical Review A - Atomic, Molecular, and Optical Physics
 |
| ISSN | 1050-2947 |
| Volume | 85Issue:4Pages:- |
| English Abstract | Physical properties of the ground and excited states of a k-local Hamiltonian are largely determined by the k-particle reduced density matrices (k-RDMs), or simply the k-matrix for fermionic systems-they are at least enough for the calculation of the ground-state and excited-state energies. Moreover, for a nondegenerate ground state of a k-local Hamiltonian, even the state itself is completely determined by its k-RDMs, and therefore contains no genuine k-particle correlations, as they can be inferred from k-particle correlation functions. It is natural to ask whether a similar result holds for nondegenerate excited states. In fact, for fermionic systems, it has been conjectured that any nondegenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any nondegenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure n-particle states. We construct explicit counterexamples to show that both conjectures are false. We further show that any nondegenerate excited state of a k-local Hamiltonian is a unique ground state of another 2k-local Hamiltonian, hence is uniquely determined by its 2k-RDMs (or 2k-matrix). These results set up a solid framework for the study of excited-state properties of many-body systems. © 2012 American Physical Society.; Physical properties of the ground and excited states of a k-local Hamiltonian are largely determined by the k-particle reduced density matrices (k-RDMs), or simply the k-matrix for fermionic systems-they are at least enough for the calculation of the ground-state and excited-state energies. Moreover, for a nondegenerate ground state of a k-local Hamiltonian, even the state itself is completely determined by its k-RDMs, and therefore contains no genuine k-particle correlations, as they can be inferred from k-particle correlation functions. It is natural to ask whether a similar result holds for nondegenerate excited states. In fact, for fermionic systems, it has been conjectured that any nondegenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any nondegenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure n-particle states. We construct explicit counterexamples to show that both conjectures are false. We further show that any nondegenerate excited state of a k-local Hamiltonian is a unique ground state of another 2k-local Hamiltonian, hence is uniquely determined by its 2k-RDMs (or 2k-matrix). These results set up a solid framework for the study of excited-state properties of many-body systems. © 2012 American Physical Society. |
| Indexed Type | EI |
| Keyword | Excited States Ground State Molecular Physics |
| Department | (1) Department of Mathematics and Statistics University of Guelph Guelph ON Canada; (2) Institute for Quantum Computing School of Computer Science University of Waterloo Waterloo ON Canada; (3) State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences Beijing China; (4) Centre for Quantum Technologies National University of Singapore Singapore 117543 Singapore; (5) Institute for Quantum Computing University of Waterloo Waterloo ON Canada |
| Language | 英语 |
| WOS ID | WOS:000302600200001 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/15464 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Chen Jianxin,Ji Zhengfeng,Wei Zhaohui,et al. correlations in excited states of local hamiltonians[J]. Physical Review A - Atomic, Molecular, and Optical Physics,2012,85(4):-. |
| APA | Chen Jianxin,Ji Zhengfeng,Wei Zhaohui,&Zeng Bei.(2012).correlations in excited states of local hamiltonians.Physical Review A - Atomic, Molecular, and Optical Physics,85(4),-. |
| MLA | Chen Jianxin,et al."correlations in excited states of local hamiltonians".Physical Review A - Atomic, Molecular, and Optical Physics 85.4(2012):-. |
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