Reduced density matrices/static correlation functions of Richardson–Gaudin states without rapidities

Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson–Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical picture, clean expressions for reduced density matrix (RDM) eleme...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of chemical physics 2022-12, Vol.157 (21), p.214104-214104
Main Authors: Faribault, Alexandre, Dimo, Claude, Moisset, Jean-David, Johnson, Paul A.
Format: Article
Language:English
Subjects:
Chemical Sciences
Density
Eigenvalues
Eigenvectors
Interpolation
Physics
Polynomials
Wave functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson–Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical picture, clean expressions for reduced density matrix (RDM) elements, and systematic improvement (with a complete set of eigenvectors). Known expressions for the RDM elements require the computation of rapidities, which are obtained by first solving for the so-called eigenvalue based variables (EBV) and then root-finding a Lagrange interpolation polynomial. In this paper, we obtain expressions for the RDM elements directly in terms of the EBV. The final expressions can be computed at the same cost as the rapidity expressions. Therefore, except, in particular, circumstances, it is entirely unnecessary to compute rapidities at all. The RDM elements require numerically inverting a matrix, and while this is usually undesirable, we demonstrate that it is stable, except when there is degeneracy in the single-particle energies. In such cases, a different construction would be required.
ISSN:0021-9606
1089-7690
DOI:10.1063/5.0123911