  The antiferromagnetic Heisenberg model on an anisotropic kagome lattice may
be a good minimal model for real magnetic systems as well as a limit from which
the isotropic case can be better understood. We therefore study the
nearest-neighbor Heisenberg antiferromagnet on an anisotropic kagome lattice in
a magnetic field. Such a system should be well described by weakly interacting
spin chains, and we motivate a general form for the interaction by symmetry
considerations and by perturbatively projecting out the inter-chain spins. In
the spin 1/2 case, we find that the system exhibits a quantum phase transition
from a ferrimagnetic ordered state to an XY ordered state as the field is
increased. Finally, we discuss the appearance of magnetization plateaux in the
ferrimagnetic phase.
