The renormalisation group for the truncated conformal space approach on the cylinder

TL;DR

This paper advances the truncated conformal space approach by analyzing bulk perturbations, deriving renormalisation corrections, and demonstrating improved predictive accuracy for certain conformal field theories.

Contribution

It provides explicit expressions for leading truncation corrections and applies RG improvements to enhance TCSA predictions for bulk perturbations.

Findings

RG corrections improve TCSA spectrum predictions

Predicted divergence of spectrum for perturbations > 3/4

Ratios of excitation energies converge despite spectrum divergence

Abstract

In this paper we continue the study of the truncated conformal space approach to perturbed conformal field theories, this time applied to bulk perturbations and focusing on the leading truncation-dependent corrections to the spectrum. We find expressions for the leading terms in the ground state energy divergence, the coupling constant renormalisation and the energy rescaling. We apply these methods to problems treated in two seminal papers and show how these RG improvements greatly increase the predictive power of the TCSA approach. One important outcome is that the TCSA spectrum of excitations is predicted not to converge for perturbations of conformal weight greater than 3/4, but the ratios of excitation energies should converge.