Frustrated antiferromagnets at high fields: the Bose-Einstein condensation in degenerate spectra

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Quantum phase transition at the saturation field is studied for a class of frustrated quantum antiferromagnets. The considered models include (i) the J₁-J₂ frustrated square-lattice antiferromagnet with J₂=1/2J₁ and (ii) the nearest-neighbor Heisenberg antiferromagnet on a face centered cubic lattice. In the fully saturated phase the magnon spectra for the two models have lines of degenerate minima. Transition into partially magnetized state is treated via a mapping to a dilute gas of hard core bosons and by complementary spin-wave calculations. Momentum dependence of the exact four-point boson vertex removes the degeneracy of the single-particle excitation spectra and selects the ordering wave-vectors at (π,π) and (π,0,0) for the two models. The asymptotic behavior of the magnetization curve differs significantly from that of conventional antiferromagnet in d-spatial dimensions. We predict a unique form for the magnetization curve ΔM=S-M≃ μ⁽ᵈ⁻¹⁾/²(μ)⁽ᵈ⁻¹⁾, where μ is a distance from the quantum critical point.