We will discuss a recent reformulation of quantum embedding suitable for coupling a fragment of a system with long-range interactions into its environment. Treating these long-range interactions in a practical and efficient way is (I believe) the biggest conceptual and practical limitation of quantum embedding of interacting systems. Current approaches often rely on uncontrolled approximations and lack the systematic improvability to ensure trust and internal checks on the validity of results. The approach will relate to a number of existing methodology in the field, including the embedding of fragments into both mean-field and interacting environments, and detail an approach to systematically fold these interactions with the infinite environment into a finite-size quantum problem.
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