Nonperturbative study of the two-frequency sine-Gordon model
Z. Bajnok, L. Palla, G. Takacs, F. Wagner
TL;DR
This work analyzes the nonintegrable two-frequency sine-Gordon (DSG) model by combining form factor perturbation theory (FFPT) and truncated conformal space approach (TCSA). It demonstrates consistent results between FFPT and TCSA in perturbative regimes and uses TCSA to nonperturbatively explore a conjectured second-order phase transition in the rational-frequency DSG, identifying an Ising-universality Ising fixed point via finite-volume spectra and UV–IR operator correspondence. A detailed phase diagram for the special case $α/β=1/2$ is developed, showing a continuous transition and Ising-like scaling in the infrared, with a careful discussion of Runaway states and finite-volume signatures. The study also constructs a robust framework for extracting vacuum energies, masses, and IR data from TCSA, and highlights the UV-IR correspondence as a key check of the nonperturbative dynamics in a nonintegrable QFT.
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.