Contractor-renormalization approach to frustrated magnets in a magnetic field

We propose to use the contractor-renormalization (CORE) technique in order to derive effective models for quantum magnets in a magnetic field. CORE is a powerful nonperturbative technique that can reduce the complexity of a given microscopic model by focusing on the low-energy part. We provide a detailed analysis of frustrated spin ladders, which have been widely studied in the past: in particular, we discuss how to choose the building block and emphasize the use of their reduced density matrix. With a good choice of basis, CORE is able to reproduce the existence or not of magnetization plateaux in the whole phase diagram contrary to a usual perturbation theory. We also address the issue of plateau formation in two-dimensional bilayers and point out the analogy between nonfrustrated strongly anisotropic models and frustrated SU(2) ones.