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We present an inhomogeneous dynamical mean field theory (I-DMFT) that issuitable to investigate electron-lattice interactions in non-translationallyinvariant and/or inhomogeneous systems. The presented approach, whose onlyassumption is that of a local, site-dependent self-energy, recovers both theexact solution of an electron in a generic external potential in thenon-interacting limit and the DMFT solution for the small polaron problem intranslationally invariant systems. To illustrate its full capabilities, we useI-DMFT to study the effects of defects embedded on a two-dimensional surface.The computed maps of the local density of states reveal Friedel oscillations,whose periodicity is determined by the polaron mass. This can be of directrelevance for the interpretation of scanning-tunneling microscopy (STM)experiments on systems with sizable electron-lattice interactions. Overall, theeasy numerical implementation of the method, yet full self-consistency, allowsone to study problems in real-space that were previously difficult to access.

Inhomogeneous dynamical mean field theory of the small polaron problem