Plaquette valence bond solid in the frustrated Heisenberg quantum   antiferromagnet on the square lattice
  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-1/2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (J1-J2-J3 model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)/J1=1/2, 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 solid order in part of the magnetically disordered region. 
M. Mambrini, A. Laeuchli, D. Poilblanc, F. Mila