Extended bound states in the J-1 - J2 - δ

Full text: The dimerized Heisenberg chain with second neighbor interaction, the J1 - J2 - δ model, has attracted considerable interest recently, mainly because of its relevance to a variety of quasi-one-dimensional materials. The Hamiltonian for this model reads, H = J [(1 + (-1i ) δ) Si ?Si=1 + αSi ?Si+2] where the Si are again spin-1/2 operators at site i, a parameterizes a next-nearest neighbor coupling and δ is the alternating dimerization. Depending on the coupling parameters, this model exhibits various phases including a spin-liquid gapless phase, and a dimerized gapped phase. Another interesting feature is the existence of well defined bound states below the continuum. Using the very powerful linked-cluster perturbation expansion for multi-particle spectra which has been developed recently, we have carried out the perturbation expansion for the 2-particle singlet, triplet and quintet states to 19th order. Our high order calculations produce qualitatively unexpected results. There are multiple bound states with S=0, 1 and 2 even in the weakly-coupled dimer limit. The number of bound states varies with frustration, and many of them only show up when the expansions are done to sufficiently high order. This presumably is due to the extended range of the attractive interaction needed to see the multiple bound states. The interval of k-values where the bound states exist also changes with the expansion parameter. Some of these bound states have not been reported by previous calculations, most likely due to a limited precision or a general incapability to deal with multiple bound states