We introduce Extended Density Matrix Embedding Theory (EDMET), a static quantum embedding theory explicitly self-consistent with respect to two-body environmental interactions. This overcomes the biggest practical and conceptual limitation of more traditional one-body embedding methods, namely the lack of screening and treatment of long-range correlations. This algebraic zero-temperature embedding augments the correlated cluster with a minimal number of bosons from the random phase approximation, and admits an analytic approach to build a self-consistent Coulomb-exchange-correlation kernel. For extended Hubbard models with non-local interactions, this leads to the accurate description of phase transitions, static quantities and dynamics. We also move towards {em ab initio} systems via the Parriser--Parr--Pople model of conjugated coronene derivatives, finding good agreement with experimental optical gaps.
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