Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevA.85.040303
Title: Correlations in excited states of local Hamiltonians
Authors: Chen, J.
Ji, Z.
Wei, Z. 
Zeng, B.
Issue Date: 9-Apr-2012
Citation: Chen, J., Ji, Z., Wei, Z., Zeng, B. (2012-04-09). Correlations in excited states of local Hamiltonians. Physical Review A - Atomic, Molecular, and Optical Physics 85 (4) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevA.85.040303
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.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/116275
ISSN: 10502947
DOI: 10.1103/PhysRevA.85.040303
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