Nonlinear bond-operator theory and1/dexpansion for coupled-dimer magnets. II. Antiferromagnetic phase and quantum phase transition

Abstract

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 intradimer coupling, we connect our approach to spin-wave theory.