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Renormalization methods in truncated conformal space with applications

Máté Lencsés

Published Jan 1, 2015• 0 citations
Publisher
DOI
10.15476/elte.2015.156

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arXiv:1405.3157•Journal of High Energy Physics•Sep 1, 2014•49 citations
We discuss the errors introduced by level truncation in the study of boundary renormalization group (RG) flows using the truncated conformal space approach (TCSA). 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 ϕ (13) , we propose a RG 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 thermodynamic Bethe ansatz equations.
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.
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.