Excitation spectrum of the S=1/2 quantum spin ladder with frustration: Elementary quasiparticles and many-particle bound states

The excitation spectrum of the two-chain S = 1/2 Heisenberg spin ladder wit h additional second neighbor frustrating interactions is studied by a varie ty df techniques. A description. based on a mapping of the model onto a Bos e gas of hard-core triplets is used to determine the one- and two-particle excitation spectra. We find that low-lying singlet and triplet bound states are present and their binding energy increases with increasing frustration . In addition, many-particle bound states are found by exact diagonalizatio n and variational methods. We prove that the larger the number of bound par ticles the larger the binding energy. Thus the excitation spectrum has a co mplex structure and consists of elementary triplets and composite many-part icle singlet and triplet bound stales. The composite excitations mix strong ly with the elementary ones in the coupling regime where quantum fluctuatio ns are strong. The quantum phase transition, known to take place in this mo del at critical frustration, is interpreted as a condensation process of (i nfinitely) large many-particle bound states. [S0163-1829(99)02609-0].