A variational method for integrability-breaking Richardson-Gaudin models

TL;DR

This paper introduces a variational approach that leverages integrable Richardson-Gaudin models to approximate ground states of nearly integrable spin systems, outperforming perturbation theory especially near integrability-breaking interactions.

Contribution

The paper develops a novel variational method that optimizes eigenstates of Richardson-Gaudin models to effectively approximate non-integrable spin models, including handling level crossings.

Findings

Exact results for integrable models

Significant improvement over perturbation theory near integrability

Effective description of non-integrable models with level crossings

Abstract

We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of integrability allows for an efficient evaluation and minimization of the energy functional. The method is shown to return exact results for integrable models and improve substantially on perturbation theory for models close to integrability. For large integrability-breaking interactions, it is shown how (avoided) level crossings necessitate the use of excited states of integrable Hamiltonians in order to accurately describe the ground states of general non-integrable models.