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

TL;DR

This paper demonstrates that Richardson-Gaudin states can accurately approximate seniority-zero ground and excited states in strongly-correlated electronic systems using a variational approach, with a focus on selecting the correct RG state.

Contribution

It introduces a method to effectively use Richardson-Gaudin states for accurate variational approximation of seniority-zero states, including excited states, by proper state selection.

Findings

RG states provide good approximation for seniority-zero states

Correct state selection is crucial for accuracy

Variational ground state solution guides state choice

Abstract

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer 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 un-physical behaviour but in this contribution it is shown that with only the variational solution for the ground state, all the seniority-zero states are quite well approximated. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice and we expect it should always be possible to reason physically which state to choose.