  We introduce Extended Density Matrix Embedding Theory (EDMET), a static
quantum embedding theory explicitly self-consistent with respect to local
two-body physics. This overcomes the biggest practical and conceptual
limitation of more traditional one-body embedding methods, namely the lack of
screening and treatment of longer-range interactions. This algebraic
zero-temperature embedding augments a local interacting cluster model with a
minimal number of bosons from a description of the full system correlations via
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 ab
initio systems via the Parriser--Parr--Pople model of conjugated coronene
derivatives, finding good agreement with experimental optical gaps.
