The Elliptic Gaudin Model: a Numerical Study

TL;DR

This paper extends the exact solution of the elliptic Gaudin model to arbitrary spins and investigates its properties numerically, proposing a new integrable anisotropic central spin model for large systems.

Contribution

It generalizes the elliptic Gaudin model's exact solution to arbitrary spins and introduces a new integrable anisotropic central spin model.

Findings

Numerical analysis of Bethe roots for systems with three different spins.

Proposal and numerical study of a new integrable anisotropic central spin model.

Demonstration of the model's applicability to large systems.

Abstract

The elliptic Gaudin model describes completely anisotropic spin systems with long range interactions. The model was proven to be quantum integrable by Gaudin and latter the exact solution was found by means of the algebraic Bethe ansatz. In spite of the appealing properties of the model, it has not yet been applied to any physical problem. We here generalize the exact solution to systems with arbitrary spins, and study numerically the behavior of the Bethe roots for a system with three different spins. Then, we propose an integrable anisotropic central spin model that we study numerically for very large systems.