# Lattice approach to finite volume form-factors of the Massive Thirring/Sine-Gordon model

## TL;DR

This paper develops a lattice approach using quantum inverse scattering to compute finite volume form-factors in the Massive Thirring/Sine-Gordon model, providing new conjectures for expectation values of local operators.

## Contribution

It introduces a lattice framework for calculating finite volume form-factors and proposes an exact expression for local operator expectation values in soliton states.

## Key findings

- Computed finite volume diagonal matrix elements of the U(1) current.
- Conjectured an exact formula for finite volume expectation values.
- Identified exponential corrections differing from previous TBA conjectures.

## Abstract

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the $U(1)$ conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.