  Density matrix embedding theory (Phys. Rev. Lett. 109, 186404 (2012)) and
density embedding theory ((Phys. Rev. B 89, 035140 (2014)) have recently been
introduced for model lattice Hamiltonians and molecular systems. In the present
work, the formalism is extended to the ab initio description of infinite
systems. An appropriate definition of the impurity Hamiltonian for such systems
is presented and demonstrated in cases of 1, 2 and 3 dimensions, using coupled
cluster theory as the impurity solver. Additionally, we discuss the challenges
related to disentanglement of fragment and bath states. The current approach
yields results comparable to coupled cluster calculations of infinite systems
even when using a single unit cell as the fragment. The theory is formulated in
the basis of Wannier functions but it does not require separate localization of
unoccupied bands. The embedding scheme presented here is a promising way of
employing highly accurate electronic structure methods for extended systems at
a fraction of their original computational cost.
