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Electro Thermal Transport Coefficients at Finite Frequencies

We review a recently developed formalism for computing thermoelectric coefficients in correlated matter. The usual difficulties of such a calculation are circumvented by a careful generalization the transport formalism to finite frequencies, from which one can extract the high frequency objects. The technical parallel between the Hall constant and the Seebeck coefficient is explored and used to advantage. For small clusters, exact diagonalization gives the full spectrum for the Hubbard and especially the $t$-$J$ model, a prototypical model for strong correlations, and this spectrum can be used to compute the exact finite frequency transport coefficients and hence to benchmark various approximations. An application of this formalism to the physically important case of sodium cobaltate $Na_xCoO_2$ is made, and interesting predictions for new materials are highlighted.