S=12 chain-boundary excitations in the Haldane phase of one-dimensional S=1 systems

The S=12 chain-boundary excitations occurring in the Haldane phase of 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<~β<~1. At the Affleck-Kennedy-Lieb-Tasaki point, β=-13, 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/ln3, and that the on-site magnetization for the first site is 〈S1z〉=23. Applying the density matrix renormalization group we show that the chain-boundary excitations remain localized at the boundaries for -1<β<1. As the two critical points β=±1 are approached the size of the S=12 objects diverges and their amplitude appears to vanish.