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The elementary excitation in the antiferromagnetic spin-1 model known as theAffleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian has been described alternativelyas magnons or kink-like solitons (triplons). The latter, which we call thetriplon throughout this paper, has been proven equivalent descriptions of thesame magnon excitation and not an independent branch of excited states. On theother hand, no careful examination of multi-magnon and multi-triplonequivalence was made in the past. In this paper we prove that two-magnon andtwo-triplon states are also identical descriptions of the same excited states,and furthermore that their energies break down as the sum of one-triplonenergies exactly for the AKLT Hamiltonian. The statement holds despite the factthat the model is non-integrable. Such magnon/triplon dichotomy is conjecturedto hold for arbitrary n-magnon and n-triplon states. The one- and two-triplonstates form orthogonal sets that can be used to span the low-energy Hilbertspace. We construct an effective version of the AKLT Hamiltonian within suchsubspace, and work out the correction to the one-triplon energy gap that findsexcellent agreement with the known exact value.

Low-energy dynamics of the Affleck-Kennedy-Lieb-Tasaki model in the one- and two-triplon basis