  We present a robust scheme to derive effective models non-perturbatively for
quantum lattice models when at least one degree of freedom is gapped. A
combination of graph theory and the method of continuous unitary
transformations (gCUTs) is shown to efficiently capture all zero-temperature
fluctuations in a controlled spatial range. The gCUT can be used either for
effective quasi-particle descriptions or for effective low-energy descriptions
in case of infinitely degenerate subspaces. We illustrate the method for 1d and
2d lattice models yielding convincing results in the thermodynamic limit. We
find that the recently discovered spin liquid in the Hubbard model on the
honeycomb lattice lies outside the perturbative strong-coupling regime. Various
extensions and perspectives of the gCUT are discussed.
