Properties of the massive Thirring model from the XYZ spin chain

TL;DR

This paper uses the XYZ spin chain to study the massive Thirring model, calculating particle mass ratios and conformal dimensions, confirming duality relations and contrasting with recent numerical approaches.

Contribution

It provides numerical results for mass ratios and conformal dimensions of the massive Thirring model from the XYZ spin chain, supporting the duality with the sine-Gordon model.

Findings

Mass ratios agree with the DHN formula.

Results differ from recent Bethe ansatz calculations.

Confirms duality between the Thirring and sine-Gordon models.

Abstract

We consider here the massive Thirring model regularized with the XYZ spin chain. We numerically calculate the mass ratios of particles which lie in the discrete part of the spectrum and obtain results in accordance 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 and evaluate the conformal dimensions. This paper, taken together with the previous one for the sine-Gordon model, confirms the duality relation between two models formulated by Klassen and Melzer [Int. J. Mod. Phys. A 8, 4131 (1993)].