THE ANTIFERROMAGNETIC SPIN-1 2 CHAIN WITH COMPETING DIMERS AND PLAQUETTES - NUMERICAL VERSUS EXACT RESULTS/

We examine the ground state and the excitations of a one-dimensional H eisenberg spin-1/2 antiferromagnet with alternating dimers and four-sp in plaquettes (a dimer-plaquette chain). The properties of the system depend on the competing dimer and plaquette bonds. Several exact, exac t numerical and perturbational results are presented. We find that the system is gapped for ail parameter values. The spin pair correlation functions can be characterized by three different correlation lengths for dimer-dimer, dimer-plaquette and plaquette-plaquette correlations. For the latter we find an effective S = 1 Haldane-like behaviour in t he limit of dominating dimer bonds. On introducing frustration, the sy stem undergoes a first-order phase transition to a fully dimerized sta te. As regards the phase relationships of the ground-state wave functi on, the system represents an example showing exact validity of the Mar shall-Peierls sign rule in a strongly frustrated antiferromagnet. The model considered is related to the recently found 1/5-depleted square- lattice Heisenberg system CaV4O9.