On the renormalisation group for the boundary truncated conformal space approach

TY - JOUR

T1 - On the renormalisation group for the boundary truncated conformal space approach

AU - Watts, Gerard M. T.

PY - 2012/6/11

Y1 - 2012/6/11

N2 - 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 now. Finally we study the large coupling behaviour of TCSA and show that it accurately encompasses several different fixed points. (C) 2012 Elsevier B.V. All rights reserved.

AB - 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 now. Finally we study the large coupling behaviour of TCSA and show that it accurately encompasses several different fixed points. (C) 2012 Elsevier B.V. All rights reserved.

U2 - 10.1016/j.nuclphysb.2012.01.012

DO - 10.1016/j.nuclphysb.2012.01.012

M3 - Article

VL - 859

SP - 177

EP - 206

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2

ER -