Ground-state energy of a Richardson-Gaudin integrable BCS model

TL;DR

This paper derives an integral equation for the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing previous models, and confirms its consistency with BCS mean-field results.

Contribution

It introduces a generalized integrable BCS model with conserved operators and derives a continuum limit integral equation for the ground state energy.

Findings

Integral equation for ground-state energy established

Energy matches BCS mean-field results

Generalizes closed and open p+ip models

Abstract

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.