Nonperturbative study of the two-frequency sine-Gordon model

TL;DR

This paper investigates the two-frequency sine-Gordon model, especially at a 1/2 frequency ratio, using both perturbative and nonperturbative methods to analyze phase transitions and operator correspondences.

Contribution

It provides the first nonperturbative evidence that the phase transition is second order and in the Ising universality class for this model.

Findings

The phase transition is of second order.

The transition belongs to the Ising universality class.

The phase diagram of the model is conjectured.

Abstract

The two-frequency sine-Gordon model is examined. The focus is mainly on the case when the ratio of the frequencies is 1/2, given the recent interest in the literature. We discuss the model both in a perturbative (form factor perturbation theory) and a nonperturbative (truncated conformal space approach) framework, and give particular attention to a phase transition conjectured earlier by Delfino and Mussardo. We give substantial evidence that the transition is of second order and that it is in the Ising universality class. Furthermore, we check the UV-IR operator correspondence and conjecture the phase diagram of the theory.