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 (31)
- Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
- Seniority-based coupled cluster theory
- Can single-reference coupled cluster theory describe static correlation?
- Efficient description of strongly correlated electrons with mean-field cost
- 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
- Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz
- An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis
- Linearized Coupled Cluster Correction on the Antisymmetric Product of 1 reference orbital Geminals
- The Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
- An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
- Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models
- Solving the Richardson equations for Fermions
- Exact mesoscopic correlation functions of the pairing model
- Analysis of two-orbital correlations in wavefunctions restricted to electron-pair states
- Correlating AGP on a quantum computer
- Geminal-Based Configuration Interaction
- Correlating the Antisymmetrized Geminal Power Wave Function
- Efficient evaluation of AGP reduced density matrices
- Richardson-Gaudin integrability in the contraction limit of the quasispin
- Orbital entanglement and correlation from pCCD-tailored Coupled Cluster wave functions
- Geminal replacement models based on AGP
- Exploring non-linear correlators on AGP
- Why scalar products in the algebraic Bethe ansatz have determinant representation
- Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction
- Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems
- Exact expectation values within Richardson's approach for the pairing Hamiltonian in a macroscopic system
- "Probabilistic" approach to Richardson equations
- A variational method for integrability-breaking Richardson-Gaudin models
- Richardson-Gaudin Configuration-Interaction for nuclear pairing correlations