6533b7cffe1ef96bd1258fba
RESEARCH PRODUCT
Long-range interactions and the sign of natural amplitudes in two-electron systems
Robert Van LeeuwenKlaas J. H. Giesbertzsubject
Atomic Physics (physics.atom-ph)General Physics and AstronomyInteraction strengthFOS: Physical sciences02 engineering and technologyElectron01 natural sciencesPhysics - Atomic PhysicsCondensed Matter - Strongly Correlated Electronssymbols.namesakeQuantum mechanics0103 physical sciencesCoulombPhysical and Theoretical ChemistryWave functionPhysicsQuantum Physicsta114010304 chemical physicsStrongly Correlated Electrons (cond-mat.str-el)Avoided crossingComputational Physics (physics.comp-ph)021001 nanoscience & nanotechnologyAmplitudesymbolsReduced density matrix0210 nano-technologyHamiltonian (quantum mechanics)Quantum Physics (quant-ph)Physics - Computational Physicsdescription
In singlet two-electron systems the natural occupation numbers of the one-particle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the two-electron wave function in a natural orbital basis. In this work we relate the sign of the natural amplitudes to the nature of the two-body interaction. We show that long-range Coulomb-type interactions are responsible for the appearance of positive amplitudes and give both analytical and numerical examples that illustrate how the long-distance structure of the wave function affects these amplitudes. We further demonstrate that the amplitudes show an avoided crossing behavior as function of a parameter in the Hamiltonian and use this feature to show that these amplitudes never become zero, except for special interactions in which infinitely many of them can become zero simultaneously when changing the interaction strength. This mechanism of avoided crossings provides an alternative argument for the non-vanishing of the natural occupation numbers in Coulomb systems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-09-01 |