Quantum Monte-Carlo simulation of spin-one antiferromagnets with single-ion anisotropy

We study a spin-one Heisenberg model with uniaxial single-ion anisotropy, $D$, and Zeeman coupling to a magnetic field, B, parallel to the symmetry axis. We compute the $(D/J, B/J)$ quantum phase diagram for square and simple cubic lattices by combining analytical and Quantum Monte Carlo approaches, and find a transition between XY-antiferromagnetic and ferronematic phases that spontaneously break the U(1) symmetry of the model. In the language of bosonic gases, this is a transition between a Bose-Einstein condensate (BEC) of single bosons and a BEC of pairs. For the efficient simulation of ferronematic phase, we developed and implemented a new multi-discontinuity algorithm based on the directed-loop algorithm. The ordinary quantum Monte-Carlo methods fall into freezing problems when we apply them to this system at large $D/J$ and finite $B/J\sim 1$. The new method does not suffer from the freezing problems.