Norm of Bethe-wave functions in the continuum limit

TL;DR

This paper derives a formula for the norm of Bethe-wave functions in the 6-vertex model's continuum limit, connecting lattice states to sine-Gordon soliton states and showing the norm's relation to the Gaudin-determinant.

Contribution

It provides a new expression for Bethe-wave function norms in the continuum limit, linking lattice models to sine-Gordon soliton states and their determinants.

Findings

The norm formula's determinant part expands in large volume limit.

The determinant is proportional to the Gaudin-determinant of sine-Gordon soliton states.

The results connect lattice Bethe states to continuum sine-Gordon models.

Abstract

The 6-vertex model with appropriately chosen alternating inhomogeneities gives the so-called light-cone lattice regularization of the sine-Gordon (Massive-Thirring) model. In this integrable lattice model we consider pure hole states above the antiferromagnetic vacuum and express the norm of Bethe-wave functions in terms of the hole's positions and the counting-function of the state under consideration. In the light-cone regularized picture pure hole states correspond to pure soliton (fermion) states of the sine-Gordon (massive Thirring) model. Hence, we analyze the continuum limit of our new formula for the norm of the Bethe-wave functions. We show, that the physically most relevant determinant part of our formula can be expanded in the large volume limit and turns out to be proportional to the Gaudin-determinant of pure soliton states in the sine-Gordon model defined in finite volume.