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

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 $=2/3$. 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.