$S=1/2$ Chain-Boundary Excitations in the Haldane Phase of 1D $S=1$ Systems

TL;DR

This study investigates boundary excitations in the Haldane phase of spin-1 chains, revealing their localization properties, dependence on the biquadratic interaction, and behavior near critical points using analytical and numerical methods.

Contribution

It provides a detailed analysis of boundary excitations in the Haldane phase, showing their localization and evolution across different interaction strengths using DMRG and analytical calculations.

Findings

Boundary excitations are localized at chain ends at the AKLT point.

Localization persists across the entire range of biquadratic interactions.

Excitations diverge and vanish as critical points are approached.

Abstract

The $s=1/2$ chain-boundary excitations occurring in the Haldane phaseof $s=1$ antiferromagnetic spin chains are investigated. The bilinear-biquadratic hamiltonian is used to study these excitations as a function of the strength of the biquadratic term, $\beta$, between $-1\le\beta\le1$. At the AKLT point, $\beta=-1/3$, we show explicitly that these excitations are localized at the boundaries of the chain on a length scale equal to the correlation length $\xi=1/\ln 3$, and that the on-site magnetization for the first site is $<S^z_1>=2/3$. Applying the density matrixrenormalization group we show that the chain-boundaryexcitations remain localized at the boundaries for $-1\le\beta\le1$. As the two critical points $\beta=\pm1$ are approached the size of the $s=1/2$ objects diverges and their amplitude vanishes.