Phase transitions and entanglement properties in spin-1 Heisenberg   clusters with single-ion anisotropy
  The incipient quantum phase transitions of relevance to nonzero fluctuations and entanglement in Heisenberg clusters are studied in this paper by exploiting negativity as a measure in bipartite and frustrated spin-1 anisotropic Heisenberg clusters with bilinear-biquadratic exchange, single-ion anisotropy and magnetic field. Using the exact diagonalization technique, it is shown that quantum critical points signaled by qualitative changes in behavior of magnetization and particle number are ultimately related to microscopic entanglement and collective excitations. The plateaus and peaks in spin and particle susceptibilities define the conditions for a high/low-density quantum entanglement and various ordered phases with different spin (particle) concentrations. 
V S Abgaryan, N S Ananikian, L N Ananikyan and A N Kocharian
cond-mat.stat-mech quant-ph