  We develop a real-space extension of the dual fermion approach. This method
is formulated in terms of real-space Green's functions and local vertex
functions, which enables us to discuss local and nonlocal correlations in
inhomogeneous systems with an arbitrary geometric structure. We first
demonstrate that the approach gives us reasonable results for a homogenous
periodic system by taking into account onsite and nearest-neighbor intersite
correlations. Moreover, we study the half-filled Hubbard model on the
quasiperiodic Penrose lattice and clarify the role of intersite correlations
for the Mott transition. The intersite correlations lead to a rich structure in
local observables which is inherited from the quasiperiodic structure of the
lattice.
