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We present a robust scheme to derive effective models non-perturbatively forquantum lattice models when at least one degree of freedom is gapped. Acombination of graph theory and the method of continuous unitarytransformations (gCUTs) is shown to efficiently capture all zero-temperaturefluctuations in a controlled spatial range. The gCUT can be used either foreffective quasi-particle descriptions or for effective low-energy descriptionsin case of infinitely degenerate subspaces. We illustrate the method for 1d and2d lattice models yielding convincing results in the thermodynamic limit. Wefind that the recently discovered spin liquid in the Hubbard model on thehoneycomb lattice lies outside the perturbative strong-coupling regime. Variousextensions and perspectives of the gCUT are discussed.

Effective models for gapped phases of strongly correlated quantum lattice models