  Quantitative simulation of electronic structure of solids requires the
treatment of local and non-local electron correlations on an equal footing.
Dynamical mean-field theory, a widely-used quantum embedding algorithm that
assumes local self-energy approximation, is challenging to extend to capture
long-range electron correlation. In this work, we present a new formulation of
Green's function embedding that, instead of embedding the impurity in
non-interacting bath through the hybridization function, derives bath
representation with general two-particle interactions in a fully ab initio and
systematically improvable manner. The resulting interacting-bath dynamical
embedding theory (ibDET) simulates local and non-local self-energies using
high-level quantum chemistry solvers, such as the coupled-cluster theory. We
demonstrate that ibDET combined with the GW theory (GW+ibDET) achieves good
agreements with experimental band structure and photoemission spectra while
preserving translational symmetry across a range of semiconducting, insulating,
and metallic materials. Furthermore, our approach allows quantifying the role
of non-local electron correlation in determining spectral properties of
materials and addressing the long-standing debate over the bandwidth narrowing
of metallic sodium.
