  We study N=4 SYM theory coupled to fundamental N=2 hypermultiplets in a state
of finite charge density. The setup can be described holographically as a
configuration of D3 and D7 branes with a non-trivial worldvolume gauge field on
the D7. The phase has been identified as a new form of quantum liquid, where
certain properties are those of a Fermi liquid while others are clearly
distinct. We focus on the entanglement among the flavors, as quantified by the
entanglement entropy. The expectation for a Fermi liquid would be a logarithmic
enhancement of the area law, but we find a more drastic enhancement instead.
The leading contributions are volume terms with a non-trivial shape dependence,
signaling extensive entanglement among the flavors. At finite temperature these
correlations are confined to a region of size given by the inverse temperature.
