Dual Separated Variables and Scalar Products

TL;DR

This paper advances the separation of variables method for higher-rank integrable spin chains, specifically deriving the measure for the su(3) case by leveraging wave function factorisability and orthogonality relations.

Contribution

It extends the SoV framework to su(3) spin chains, providing a new derivation of the measure based on functional orthogonality and Baxter equations.

Findings

Derived the measure for su(3) spin chains using SoV

Demonstrated the role of wave function factorisability

Connected Baxter equations with orthogonality relations

Abstract

Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue developing the SoV program for higher-rank spin chains and demonstrate how to derive the measure for the su(3) case. Our results are a natural consequence of factorisability of the wave function and functional orthogonality relations following from the interplay between Baxter equations for Q-functions and their dual.