Yoshitomo Kamiya, Cristian D. Batista
The phase diagram near the magnetic field-induced quantum critical point of dimerized spin systems can be extremely rich when the interactions are frustrated. Complex phases that emerge near this critical point are derived under control by mapping the spin system into a dilute gas of bosons. Geometric frustration of the dimer lattice manifests in a rather large degeneracy of wave-vectors $\mathbf{Q}_{n}$ that minimize the single-boson dispersion. The bosons can then condense into a single or a multi-$\mathbf{Q}$ state. The magnetic counterparts of these condensates range from a simple spiral (single-$\mathbf{Q}$ condensate) to magnetic vortex crystals (6-$\mathbf{Q}$ condensates). Inspired by the S=1 dimer antiferromagnet Ba$_3$Mn$_2$O$_8$, we calculate the effective boson-boson interactions in the dilute limit and demonstrate that a plethora of exotic condensates emerge above the critical field $H=H_{c1}$ and that a six-fold symmetric exchange anisotropy selects a vortex crystal or a double-$\mathbf{Q}$ fan state.
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http://arxiv.org/abs/1303.0012
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