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Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets II: Antiferromagnetic phase and quantum phase transition

We extend to magnetically ordered phases a recently developed expansion in 1/d for coupled-dimer Heisenberg magnets, where d is the number of space dimensions. This extension utilizes generalized bond operators describing spin excitations on top of a reference state involving triplet condensates. We explicitly consider a model of dimers on a hypercubic lattice which displays, in addition to the paramagnetic singlet phase, a collinear antiferromagnetic phase for which we calculate static and dynamic observables at zero temperature. In particular, we show that the 1/d expansion smoothly connects the paramagnetic and antiferromagnetic phases and produces sensible results at and near the quantum phase transition point. Among others, we determine the dispersion and spectral-weight distribution of the amplitude (i.e. Higgs) mode of the ordered phase. In the limit of vanishing intra-dimer coupling, we connect our approach to spin-wave theory.