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Recent progress in treating the dynamically screened nature of the Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We discuss approximate and exact methods for the solution of impurity models with retarded interactions, and explain how these models appear as auxiliary problems in various extensions of the dynamical mean field formalism. The current state of the field is illustrated with results from recent applications of these schemes to U-V Hubbard models and correlated materials.
We provide a prescription for constructing Hamiltonians representing the low energy physics of correlated electron materials with dynamically screened Coulomb interactions. The key feature is a renormalization of the hopping and hybridization paramet
Recent discoveries, as well as open questions, in experimentally realized correlated electron materials are reviewed. In particular, high temperature superconductivity in the cuprates and in the recently discovered iron pnictides, possible chiral p-w
The magnetic correlations, local moments and the susceptibility in the correlated 2D Kondo lattice model at half filling are investigated. We calculate their systematic dependence on the control parameters J_K/t and U/t. An unbiased and reliable exac
We recently introduced the dynamical cluster approximation(DCA), a new technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean field approximation while preserving causality. The technique i
We present the exact Bethe Ansatz solution of a multichannel model of one- dimensional correlated electrons coupled antiferromagnetically to a magnetic impurity of arbitrary spin S. The solution reveals that interactions in the bulk make the magnetic