Title: correlations in excited states of local hamiltonians

Author: Chen Jianxin
; Ji Zhengfeng
; Wei Zhaohui
; Zeng Bei
Keyword: Excited states
; Ground state
; Molecular physics
Source: Physical Review A - Atomic, Molecular, and Optical Physics
Issued Date: 2012
Volume: 85, Issue: 4, Pages: - Indexed Type: EI
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
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.
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.
Language: 英语
WOS ID: WOS:000302600200001
Citation statistics:

Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/15464
Appears in Collections: 软件所图书馆_期刊论文

There are no files associated with this item.

Recommended Citation:
Chen Jianxin,Ji Zhengfeng,Wei Zhaohui,et al. correlations in excited states of local hamiltonians[J]. Physical Review A - Atomic, Molecular, and Optical Physics,2012-01-01,85(4):-.