On the form factors of local operators in the lattice sine-Gordon model

TL;DR

This paper introduces a new method using Sklyanin's separation of variables to compute form factors of local operators in the lattice sine-Gordon model, providing explicit determinant formulas for matrix elements.

Contribution

It develops a novel approach combining determinant formulas and the reconstruction of local fields within the SOV framework for the sine-Gordon model.

Findings

Derived a generic determinant formula for scalar products in SOV

Reconstructed local operators in terms of separate variables

Expressed form factors as sums of determinants involving Baxter Q-operator eigenvalues

Abstract

We develop a method for computing form factors of local operators in the framework of Sklyanin's separation of variables (SOV) approach to quantum integrable systems. For that purpose, we consider the sine-Gordon model on a finite lattice and in finite dimensional cyclic representations as our main example. We first build our two central tools for computing matrix elements of local operators, namely, a generic determinant formula for the scalar products of states in the SOV framework and the reconstruction of local fields in terms of the separate variables. The general form factors are then obtained as sums of determinants of finite dimensional matrices, their matrix elements being given as weighted sums running over the separate variables and involving the Baxter Q-operator eigenvalues.