Abstract
We study a spin-1 Heisenberg model with exchange interaction $J$, uniaxial single-ion exchange 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. Our work opens up new avenues for measuring this transition in real magnets.
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