Richardson-Gaudin States

TL;DR

This chapter reviews Richardson-Gaudin states, a class of weakly correlated electron pairs, detailing solution methods, density matrix expressions, and their application to hydrogen chains within integrable models and quantum chemistry.

Contribution

It provides a comprehensive overview of Richardson-Gaudin states, including a straightforward solution method and their relevance to quantum chemistry and integrable models.

Findings

Efficient method to solve Richardson-Gaudin equations

Optimal expressions for density matrix elements

Application to 1D hydrogen chains

Abstract

This chapter gives an overview of Richardson-Gaudin states which represent weakly correlated pairs of electrons. They are parametrized by sets of numbers obtained from non-linear equations. The best method to solve these equations is presented in a straightforward manner with enough detail to implement the method computationally. Optimal expressions for the density matrix elements are discussed. A simple description of 1-dimensional hydrogen chains is presented in terms of Richardson-Gaudin states. Richardson-Gaudin states are placed in the larger context of integrable models and geminal wavefunctions of quantum chemistry.