A method to solving a strongly correlated quantum lattice model. This treats correlations along imaginary time (dynamical correlations) with accuracy but ignores spatial ones. This can exactly solve infinite dimensional models such as models on the Bethe lattice. In this method, one first reduces the original model to an impurity model (Anderson model) by dividing the original lattice model into a center site (impurity) and the surrounding sites (effective medium) . Second, one solve this impurity problem under the self-consistent condition that a Green function and a self energy of the medium are equal to those of the original lattice model. Exact diagonalization, numerical renormalization, and path-integral Monte Carlo method are used for an impurity solver. Including spatial correlations has been studied.