Excited state TBA and renormalized TCSA in the scaling Potts model

TL;DR

This paper develops a new excited state TBA system and applies a renormalized TCSA to analyze the scaling Potts model, achieving high-precision agreement and insights into low-energy scattering phenomena.

Contribution

It introduces a novel TBA system for excited states and refines the renormalized TCSA method, demonstrating their consistency and effectiveness in the Potts model.

Findings

TBA system matches TCSA results with high precision

Renormalized TCSA clarifies renormalization and counter terms

Insights into low-energy quasi-particle scattering

Abstract

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S-matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.