Transition density matrices of Richardson-Gaudin states
arXiv:2012.10477 · doi:10.1063/5.0041051
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.
References in corpus (12)
- Quasiparticle Coupled Cluster Theory for Pairing Interactions
- Projected seniority-two orbital optimization of the Antisymmetric Product of one-reference orbital Geminal
- Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
- An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis
- An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
- Analysis of two-orbital correlations in wavefunctions restricted to electron-pair states
- Richardson-Gaudin integrability in the contraction limit of the quasispin
- Geminal replacement models based on AGP
- Exploring non-linear correlators on AGP
- Why scalar products in the algebraic Bethe ansatz have determinant representation
- A variational method for integrability-breaking Richardson-Gaudin models
- Richardson-Gaudin Configuration-Interaction for nuclear pairing correlations