  The Ryu-Takayanagi conjecture establishes a remarkable connection between
quantum systems and geometry. Specifically, it relates the entanglement entropy
to minimal surfaces within the setting of AdS/CFT correspondence. This Letter
shows how this idea can be generalised to generic quantum many-body systems
within a perturbative expansion where the region whose entanglement properties
one is interested in is weakly coupled to the rest of the system. A simple
expression is derived that relates a unitary disentangling flow in an emergent
RG-like direction to the min-entropy of the region under consideration.
Explicit calculations for critical free fermions in one and two dimensions
illustrate this relation.
