ODE/IQFT correspondence for the generalized affine $\mathfrak{ sl}(2)$ Gaudin model

TL;DR

This paper introduces a generalized integrable model extending the affine (2) Gaudin system, constructs its Hamiltonians, and computes their spectrum using the ODE/IQFT approach, with implications for quantization and condensed matter physics.

Contribution

It presents a new integrable system generalizing the affine (2) Gaudin model, including Hamiltonian construction and spectral analysis within the ODE/IQFT framework.

Findings

Hamiltonians explicitly constructed

Spectrum calculated using ODE/IQFT method

Model relates to multiparametric Kondo model

Abstract

An integrable system is introduced, which is a generalization of the $\mathfrak{sl}(2)$ quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated within the ODE/IQFT approach. The model fits within the framework of Yang-Baxter integrability. This opens a way for the systematic quantization of a large class of integrable non-linear sigma models. There may also be some interest in terms of Condensed Matter applications, as the theory can be thought of as a multiparametric generalization of the Kondo model.