A case study of spin-$1$ Heisenberg model in a triangular lattice
  We study the spin-$1$ model in a triangular lattice in presence of a uniaxial anisotropy field using a Cluster Mean-Field approach (CMF). The interplay between antiferromagnetic exchange, lattice geometry and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF yields two supersolid (SS) phases compatible with those present in the spin-$1/2$ XXZ model onto which the spin-$1$ system maps. Between these two SS phases, the three-sublattice order is broken and the results of the CMF depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region. 
M. Moreno-Cardoner, H. Perrin, S. Paganelli, G. De Chiara, A. Sanpera
cond-mat.str-el cond-mat.other cond-mat.quant-gas cond-mat.stat-mech quant-ph