1. Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field
- Author
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Charles-Émile Fecteau, Samuel Cloutier, Jean-David Moisset, Jérémy Boulay, Patrick Bultinck, Alexandre Faribault, and Paul A. Johnson
- Subjects
Chemical Physics (physics.chem-ph) ,DIATOMIC-MOLECULES ,Strongly Correlated Electrons (cond-mat.str-el) ,QUANTUM-MECHANICS ,SEPARATED PAIR APPROXIMATION ,General Physics and Astronomy ,FOS: Physical sciences ,CONFIGURATION-INTERACTION METHOD ,Condensed Matter - Strongly Correlated Electrons ,Chemistry ,ANTISYMMETRIC PRODUCTS ,Physics and Astronomy ,ORBITAL EXPANSION ,Physics - Chemical Physics ,WAVE-FUNCTIONS ,MATRIX RENORMALIZATION-GROUP ,ELECTRON ,Physical and Theoretical Chemistry ,GENERALIZED PRODUCT FUNCTIONS ,REDUCED DENSITY-MATRICES - Abstract
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose. Published under an exclusive license by AIP Publishing.
- Published
- 2022