On the renormalisation group for the boundary Truncated Conformal Space Approach

TL;DR

This paper investigates the renormalisation effects in the truncated conformal space approach for boundary conformal field theories, providing theoretical predictions and numerical validations across various models and perturbations.

Contribution

It predicts and verifies the leading-order renormalisation of coupling constants and Hamiltonians in TCSA, extending understanding to irrelevant perturbations and large coupling regimes.

Findings

Renormalisation predictions are validated for the tri-critical Ising and Yang-Lee models.

The spectrum remains accurate under renormalisation even for non-renormalisable perturbations.

Large coupling analysis reveals TCSA captures multiple fixed points.

Abstract

In this paper we continue the study of the truncated conformal space approach to perturbed boundary conformal field theories. This approach to perturbation theory suffers from a renormalisation of the coupling constant and a multiplicative renormalisation of the Hamiltonian. We show how these two effects can be predicted by both physical and mathematical arguments and prove that they are correct to leading order for all states in the TCSA system. We check these results using the TCSA applied to the tri-critical Ising model and the Yang-Lee model. We also study the TCSA of an irrelevant (non-renormalisable) perturbation and find that, while the convergence of the coupling constant and energy scales are problematic, the renormalised and rescaled spectrum remain a very good fit to the exact result, and we find a numerical relationship between the IR and UV couplings describing a particular flow. Finally we study the large coupling behaviour of TCSA and show that it accurately encompasses several different fixed points.