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For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phasetransitions, we develop a systematic expansion in 1/d, the inverse number ofspace dimensions. The expansion employs a formulation of the bond-operatortechnique and is based on the observation that a suitably chosen product-statewavefunction yields exact zero-temperature expectation values of localobservables in the d->infty limit, with corrections vanishing as 1/d. Wedemonstrate the approach for a model of dimers on a hypercubic lattice, whichgeneralizes the square-lattice bilayer Heisenberg model to arbitrary d. In thispaper, we use the 1/d expansion to calculate static and dynamic observables atzero temperature in the paramagnetic singlet phase, up to the quantum phasetransition, and compare the results with numerical data available for d=2.Contact is also made with previously proposed refinements of bond-operatortheory as well as with a perturbative expansion in the inter-dimer coupling. Ina companion paper, the present 1/d expansion will be extended to the orderedphase, where it is shown to consistently describe the entire phase diagramincluding the quantum critical point.

Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets I: Paramagnetic phase