Thermodynamic Bethe Ansatz for boundary sine-Gordon model

TL;DR

This paper develops a boundary thermodynamic Bethe ansatz approach to analyze the effective central charge in the massless boundary sine-Gordon model, revealing singularity crossing phenomena at specific boundary parameters.

Contribution

It extends the TBA method to boundary sine-Gordon models with a new focus on boundary parameter effects and singularity crossings.

Findings

Effective central charge dependence on boundary parameters

Identification of singularity crossing phenomena

Numerical validation of TBA predictions

Abstract

(R-channel) TBA is elaborated to find the effective central charge dependence on the boundary parameters for the massless boundary sine-Gordon model with the coupling constant $(8\pi) /\beta^2 = 1+ \lambda $ with $\lambda$ a positive integer. Numerical analysis of the massless boundary TBA demonstrates that at an appropriate boundary parameter range (cusp point) there exists a singularity crossing phenomena and this effect should be included in TBA to have the right behavior of the effective central charge.