Nonlinear Integral Equation and Finite Volume Spectrum of Minimal Models Perturbed by $\Phi_{(1,3)}$

TL;DR

This paper extends the nonlinear integral equation method to analyze the finite volume spectrum of perturbed minimal models, providing numerical validation and comparisons with existing TBA and TCS results.

Contribution

It introduces an NLIE approach for perturbed minimal models and completes previous studies on sine-Gordon theory, especially in the attractive regime and breather states.

Findings

NLIE accurately describes the finite volume spectrum of perturbed minimal models

Numerical results agree with TBA and TCS methods

Supports the validity of NLIE for these models

Abstract

We describe an extension of the nonlinear integral equation (NLIE) method to Virasoro minimal models perturbed by the relevant operator $\Phi_{(1,3)$. Along the way, we also complete our previous studies of the finite volume spectrum of sine-Gordon theory by considering the attractive regime and more specifically, breather states. For the minimal models, we examine the states with zero topological charge in detail, and give numerical comparison to TBA and TCS results. We think that the evidence presented strongly supports the validity of the NLIE description of perturbed minimal models.