Dual fermion method as a prototype of generic reference-system approach for correlated fermions

We present a purely diagrammatic derivation of the dual fermion scheme [Phys. Rev. B 77 (2008) 033101]. The derivation makes particularly clear that a similar scheme can be developed for an arbitrary reference system with the same interaction term, unrestricted by the locality of the reference problem, or even by its application to a lattice problem. As an example we present the computational results for the half-filled 2D Hubbard model with the choice of a $2\times2$ plaquette with periodic boundary conditions as a reference system. We observe that obtained results are in a good agreement with numerically exact lattice quantum Monte Carlo data.