Master equation for correlation functions in algebra symmetry $\mathfrak{gl}(2|1)$ related models

TL;DR

This paper develops a master equation framework for calculating correlation functions in integrable models with $rak{gl}(2|1)$ symmetry, generalizing previous results for simpler models and enabling multiple integral representations.

Contribution

It introduces sum formulae for form factors and correlation functions in $rak{gl}(2|1)$ models, extending earlier $rak{gl}(2)$ results and facilitating integral representations.

Findings

Derived sum formulae for form factors and correlation functions.

Established multiple integral representations for $rak{gl}(2|1)$ models.

Generalized previous $rak{gl}(2)$ results to superalgebra symmetry.

Abstract

We consider integrable models solved by the nested algebraic Bethe ansatz and associated with $\mathfrak{gl}(2|1)$ or $\mathfrak{gl}(3)$ algebra symmetry. The analogue of sum formulae, previously formulated for scalar products, is established for the form factors and correlation functions. These formulae are direct generalisation of the some earlier results derived for models with $\mathfrak{gl}(2)$ symmetric $R$-matrix. It is also shown that in the case of algebra symmetry $\mathfrak{gl}(2|1)$ related models such formula allows to establish a multiple integral representation for correlation functions and form factors.