TY - JOUR
AB - 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.
AU - Chen, J
AU - Ji, Z
AU - Wei, Z
AU - Zeng, B
DA - 2012/04/09
DO - 10.1103/PhysRevA.85.040303
JO - Physical Review A - Atomic, Molecular, and Optical Physics
PY - 2012/04/09
TI - Correlations in excited states of local Hamiltonians
VL - 85
Y1 - 2012/04/09
Y2 - 2019/10/18
ER -