Integrable spin-1/2 Richardson-Gaudin XYZ models in an arbitrary magnetic field

TL;DR

This paper introduces the most general integrable spin-1/2 Richardson-Gaudin XYZ models with arbitrary magnetic fields, providing a framework to compute eigenvalues and local observable expectations in fully anisotropic settings.

Contribution

It extends integrability to fully anisotropic XYZ models with arbitrary magnetic fields, relaxing previous antisymmetry constraints and explicitly constructing conserved charges.

Findings

Constructed explicit conserved charges satisfying quadratic equations

Enabled numerical treatment of anisotropic central spin models

Provided a method to compute eigenvalues and local observables

Abstract

We establish the most general class of spin-1/2 integrable Richardson-Gaudin models including an arbitrary magnetic field, returning a fully anisotropic (XYZ) model. The restriction to spin-1/2 relaxes the usual integrability constraints, allowing for a general solution where the couplings between spins lack the usual antisymmetric properties of Richardson-Gaudin models. The full set of conserved charges are constructed explicitly and shown to satisfy a set of quadratic equations, allowing for the numerical treatment of a fully anisotropic central spin in an external magnetic field. While this approach does not provide expressions for the exact eigenstates, it allows their eigenvalues to be obtained, and expectation values of local observables can then be calculated from the Hellmann-Feynman theorem.