Current operators in integrable spin chains: lessons from long range deformations

TL;DR

This paper derives exact finite volume mean values of current operators in integrable spin chains using long range deformations, applicable to models like SU(3), revealing their dependence on eigenvalues and Gaudin matrices.

Contribution

It introduces a new method based on long range deformations to compute current mean values in integrable spin chains, extending to higher rank models like SU(3).

Findings

Exact current mean values involve eigenvalues and Gaudin matrices.

Method applicable to higher rank integrable models.

Results consistent with previous findings in Heisenberg chains.

Abstract

We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain type of long range deformation of the local spin chains, which was discovered and explored earlier in the context of the AdS/CFT correspondence. This method is immediately applicable also to higher rank models: as a concrete example we derive the current mean values in the SU(3)-symmetric fundamental model, solvable by the nested Bethe Ansatz. The exact results take the same form as in the Heisenberg spin chains: they involve the one-particle eigenvalues of the conserved charges and the inverse of the Gaudin matrix.