  While the coherent potential approximation (CPA) is the prevalent method for
the study of disordered electronic systems, it fails to capture non-local
correlations and Anderson localization. To incorporate such effects, we extend
the dual fermion approach to disordered non-interacting systems using the
replica method. Results for single- and two- particle quantities show good
agreement with cluster extensions of the CPA; moreover, weak localization is
captured. As a natural extension of the CPA, our method presents an alternative
to the existing cluster theories. It can be used in various applications,
including the study of disordered interacting systems, or for the description
of non-local effects in electronic structure calculations.
