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Dressed solitonic excitations for the AKLT Hamiltonian

In contrast to the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) isotropic spin-1 Hamiltonian its elementary excitations are not known exactly in general. Based on a simple variational ansatz we construct approximate excitations in the form of dressed hidden domain walls. This allows us to give an improved upper bound for the gap of the AKLT Hamiltonian which is only 1% larger than the best currently available numerical result. We compare the oneand two-soliton dispersion curves with low-lying excitations for a chain of 16 sites as given by Fath and Solyom and find excellent agreement. Spin and string correlations are calculated and found to agree in leading order with the corresponding correlations for the bare kinks. Finally the weight of the string-ordered part of the lowest excited state is calculated and compared with the exact numerical result.