Reduced Density Matrices / Static Correlation Functions of Richardson-Gaudin States Without Rapidities

Abstract

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) then root-finding of a Lagrange interpolation polynomial. In this manuscript we obtain expressions for the RDM elements directly in terms of the EBV. The final expressions can be computed with 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.

References in corpus (18)

• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• Excited states using semistochastic heat-bath configuration interaction
• 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
• Excited States From State Specific Orbital Optimized Pair Coupled Cluster
• Variational coupled cluster for ground and excited states
• Orbital Optimization in Selected Configuration Interaction Methods
• Richardson-Gaudin integrability in the contraction limit of the quasispin
• Geminal replacement models based on AGP
• Exploring non-linear correlators on AGP
• On the determinant representations of Gaudin models' scalar products and form factors
• Inner products in integrable Richardson-Gaudin models
• Density Matrices of Seniority-Zero Geminal Wavefunctions
• Construction of linearly independent non-orthogonal AGP states
• Dynamical correlation functions of the mesoscopic pairing model

Cited by in corpus (6)

• Delving into the Catalytic Mechanism of Molybdenum Cofactors: A Novel Coupled Cluster Study
• Simple and efficient computational strategies for calculating orbital energies and pair-orbital energies from pCCD-based methods
• Seniority-Zero Canonical Transformation Theory: Reducing Truncation Error with Late Truncation
• Seniority-zero Linear Canonical Transformation Theory
• Ionization Potentials at Mean-Field Computational Cost: The Extended Koopmans' Framework for pCCD
• Seniority-zero Quadratic Canonical Transformation Theory