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

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, $β$, between $-1\leβ\le1$. At the AKLT point, $β=-1/3$, we show explicitly that these excitations are localized at the boundaries of the chain on a length scale equal to the correlation length $ξ=1/\ln 3$, 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 $-1\leβ\le1$. As the two critical points $β=\pm1$ are approached the size of the $s=1/2$ objects diverges and their amplitude vanishes.

4 Pages, 4 eps figures. Uses RevTeX 3.0. Submitted to PRB