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We use recently developed strong-coupling expansion methods to study thetwo-particle spectra for the frustrated alternating Heisenberg model,consisting of an alternating nearest neighbor antiferromagnetic exchange and auniform second neighbor antiferromagnetic exchange. Starting from the limit ofweakly coupled dimers, we develop high order series expansions for theeffective Hamiltonian in the two-particle subspace. In the limit of a strongapplied dimerization, we calculate accurately various properties of singlet andtriplet bound states and quintet antibound states. We also develop seriesexpansions for bound state energies in various sectors, which can beextrapolated using standard methods to cases where the externalbond-alternation goes to zero. We study the properties of singlet and tripletbound states in the latter limit and suggest a crucial role for the boundstates in the unbinding of triplets and deconfinement of spin-half excitations.Comment: 17 figures, revte

Deconfinement transition and bound states in frustrated Heisenberg chains: Regimes of forced and spontaneous dimerization