A study of truncation effects in boundary flows of the Ising model on a strip

TL;DR

This paper explores how truncation in the TCSA method affects the spectrum of the critical Ising model on a strip with boundary magnetic field, linking it to modifications in Hamiltonian coefficients.

Contribution

It provides a detailed quantum field theoretical analysis and compares truncation effects with Hamiltonian coefficient changes in the boundary Ising model.

Findings

Truncation effects can be interpreted as Hamiltonian coefficient modifications.

Qualitative spectrum behavior depends on the truncation method used.

Perturbative and numerical results support the proposed interpretation.

Abstract

We investigate the idea that the effect of the truncation applied in the TCSA method on the spectrum coincides with the effect of a suitable changing of the coefficients of the terms in the Hamiltonian operator. The investigation is done in the case of the critical Ising model on a strip with an external magnetic field on one of the boundaries. A detailed quantum field theoretical description of this model is also given, and we propose a description as a perturbation of the infinite coupling limit. The investigation is also carried out for a truncation method which preserves the solvability of the model. The results of perturbative and numerical calculations presented support the above idea and show that the qualitative behaviour of the truncated spectrum as a function of the coupling constant depends on the truncation method.