The bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect
  The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry breaking field as well as the emergence of novel phases. Previous studies have analyzed the effect of such uniaxial anysotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anysotropy. To this aim, we employ the density matrix renormalization group (DMRG) together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect. 
G. De Chiara, M. Lewenstein, A. Sanpera
cond-mat.quant-gas quant-ph