Laboratoire de Physique Théorique
Toulouse - UMR 5152

Using both exact diagonalizations and diagonalizations in a subset of short-range valence bond singlets, we address the nature of the groundstate of the Heisenberg spin- antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings ( model). A detailed comparison of the two approaches reveals a region along the line , where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore a careful analysis of dimer-dimer correlation functions, dimer structure factors and plaquette-plaquette correlation functions provides striking evidence for the presence of a plaquette valence bond crystal order in part of the magnetically disordered region.