XXZ spin chain in transverse field as a regularization of the sine-Gordon model

TL;DR

This paper studies the XXZ spin chain with a transverse field as a lattice regularization of the sine-Gordon model, calculating particle mass ratios and analyzing short-distance behavior using conformal perturbation theory.

Contribution

It provides new calculations of mass ratios in the XXZ spin chain perturbed by sigma^x, confirming some theoretical predictions and challenging previous conjectures on conformal dimensions.

Findings

Mass ratios agree with the DHN formula.

Results differ from recent Bethe Ansatz-based calculations.

Conformal dimension of the second breather differs from earlier conjectures.

Abstract

We consider here XXZ spin chain perturbed by the operator sigma^x (``in transverse field'') which is a lattice regularization of the sine-Gordon model. This can be shown using conformal perturbation theory. We calculated mass ratios of particles which lie in a discrete part of the spectrum and obtained results in accord with the DHN formula and in disagreement with recent calculations in literature based on numerical Bethe Ansatz and infinite momentum frame methods. We also analysed a short distance behavior of this states (UV or conformal limit). Our result for conformal dimension of the second breather state is different from the conjecture in [Klassen and Melzer, Int. J. Mod. Phys. A8, 4131 (1993)] and is consistent with this paper for other states.