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While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture nonlocal correlations and Anderson localization. To incorporate such effects, we extend the dual fermion approach to disordered systems using the replica method. The developed method utilizes the exact mapping to the dual fermion variables, and includes intersite scattering via diagrammatic perturbation theory in the dual variables. The CPA is recovered as a zeroth-order approximation. Results for single- and two-particle quantities show good agreement with a cluster extension of the CPA; moreover, weak localization is captured. As a natural extension of the CPA, our method presents an alternative to existing nonlocal cluster theories for disordered systems, and has potential applications in the study of disordered systems with electronic interactions. © 2013 American Physical Society.

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Physical Review B - Condensed Matter and Materials Physics