  Entanglement structure serves as a powerful way to characterize quantum
many-body phases. This is particularly so for gapless quantum liquids, where
entanglement-based tools provide one of the only means to systematically
characterize these complicated phases. For example, the Fermi-surface structure
of Fermi-liquids is revealed in entanglement entropy by a log-correction to the
typical boundary-law scaling of simpler quantum ground-states. In this paper, I
analyze the entanglement structure of a disordered, but delocalized diffusive
metal. Using a combination of analytic arguments and numerical calculations, I
show that, despite having the same number of extended gapless excitations as a
clean Fermi-liquid, the diffusive metal exhibits only boundary-law entanglement
scaling. This result pinpoints the sharp Fermi-surface structure, rather than
the finite density of gapless excitations, as the origin of the log-correction
in the Fermi-liquid entanglement scaling.
