Transition density matrices of Richardson-Gaudin states

TL;DR

This paper develops practical expressions for transition density matrices of Richardson-Gaudin states, enabling their use as a wavefunction basis beyond mean-field approximations in strongly correlated electron systems.

Contribution

It provides the first explicit formulas for transition density matrices of RG states and introduces an Aufbau-like principle to select important states.

Findings

Derived numerical transition density matrix expressions for RG states.

Demonstrated the importance of state selection using an Aufbau-like principle.

Applied methods to half-filled picket fence models.

Abstract

Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This wavefunction physically represents a mean-field of pairs of electrons (geminals) with a constant pairing strength. To move beyond the mean-field, one must develop the wavefunction in the basis of all the RG states. This requires both practical expressions for transition density matrices and an idea of which states are most important in the expansion. In this contribution, we present expressions for the transition density matrix elements and calculate them numerically for half-filled picket fence models. There are no Slater-Condon rules for RG states, though an analogue of the aufbau principle proves to be useful in choosing which states are important.