Boundary effects and the stability of the low energy spectrum of the AKLT model

TL;DR

This paper investigates how boundary effects influence the stability of the low-energy spectrum in the AKLT model, using a novel iterative Lie Schwinger method to control boundary-induced spectral splitting.

Contribution

Introduces a local, iterative Lie Schwinger block-diagonalization technique to analyze boundary effects on the AKLT model's low-energy spectrum.

Findings

Boundary effects can cause splitting of the ground-state energy levels.

The bulk gap remains stable under small, finite-range boundary perturbations.

The method effectively controls boundary-localized interactions.

Abstract

In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie Schwinger block-diagonalization method} which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps. This improves earlier results concerning the persistence of the so called \emph{bulk} gap in these models, besides illustrating the power of our general methods in a non-trivial application.