Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model

TL;DR

This paper develops an algebraic Bethe Ansatz method to derive determinant and integral representations for form factors and correlation functions in the cyclic eight-vertex solid-on-solid model, enabling exact finite-size calculations.

Contribution

It introduces a novel determinant formula for scalar products and form factors in the cyclic eight-vertex model using algebraic Bethe Ansatz techniques.

Findings

Determinant representation for scalar products in the cyclic case

Explicit finite-size form factors derived

Multiple integral form for two-point correlation functions

Abstract

We consider the problem of the exact computation of the correlation functions of the eight-vertex solid-on-solid model by means of the algebraic Bethe Ansatz. We compute the scalar product between a Bethe eigenstate and an arbitrary state of Bethe type and show that, in the cyclic case, it can be formulated as a single determinant of usual functions. It allows us to obtain determinant representations for finite-size form factors. By summing up over the form factors, we also give a multiple integral representation for a generating function of the two-point function.