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

We consider here the XXZ spin chain perturbed by the operator ${\sigma }^x$ (“in a transverse field”) which is a lattice regularization of the sine-Gordon model. This can be shown using conformal perturbation theory. We calculate the mass ratios of particles which lie in a discrete part of the spectrum and obtain results in accord with the DHN formula and in disagreement with recent calculations in the literature based on the numerical Bethe ansatz and infinite momentum frame methods. We also analyze the short distance behavior of these states (UV or conformal limit). Our result for conformal dimension of the second breather state is different from that conjectured by Klassen and Melzer [Int. J. Mod. Phys. A 8, 4131 (1993)] and is consistent with this paper for other states.