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Near-exact treatment of seniority-zero ground and excited states with a Richardson–Gaudin mean-field

2022; American Institute of Physics; Volume: 156; Issue: 19 Linguagem: Inglês

10.1063/5.0091338

1520-9032

Charles‐Émile Fecteau, Samuel Cloutier, Jean-David Moisset, Jérémy Boulay, Patrick Bultinck, Alexandre Faribault, Paul A. Johnson,

Quantum and electron transport phenomena

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.