The effect of a magnetic field on a gapped quantum magnet is described within the framework of the quantum dimer model. A minimal model describing the proliferation of itinerant spinons above a critical field is proposed and investigated by Lanczos exact diagonalizations and quantum Monte Carlo simulations. For both square and triangular lattices, it is shown that spinons are fully polarized and Bose condense. This offers a novel scenario of a quantum critical point in the dimer-liquid phase (triangular lattice) characterized by the continuous appearance of a spinon superfluid density, contrasting with the usual triplet condensation picture. The possible role of other spinon kinetic terms neglected in the model are discussed.
