A Renormalisation group for TCSA

TL;DR

This paper examines the errors in the Truncated Conformal Space Approach for boundary RG flows, proposing a RG equation for the coupling constant and comparing predictions with TBA data.

Contribution

It introduces a renormalisation group equation for TCSA coupling constants and analyzes the qualitative behavior of RG flows between boundary conditions.

Findings

TCSA results mimic RG flow sequences between boundary conditions

A fixed point is predicted at finite TCSA coupling for phi(13) perturbation

Predictions align with TBA data

Abstract

We discuss the errors introduced by level truncation in the study of boundary renormalisation group flows by the Truncated Conformal Space Approach. We show that the TCSA results can have the qualitative form of a sequence of RG flows between different conformal boundary conditions. In the case of a perturbation by the field phi(13), we propose a renormalisation group equation for the coupling constant which predicts a fixed point at a finite value of the TCSA coupling constant and we compare the predictions with data obtained using TBA equations.