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Entanglement structure serves as a powerful way to characterize quantummany-body phases. This is particularly so for gapless quantum liquids, whereentanglement-based tools provide one of the only means to systematicallycharacterize these complicated phases. For example, the Fermi-surface structureof Fermi-liquids is revealed in entanglement entropy by a log-correction to thetypical boundary-law scaling of simpler quantum ground-states. In this paper, Ianalyze the entanglement structure of a disordered, but delocalized diffusivemetal. Using a combination of analytic arguments and numerical calculations, Ishow that, despite having the same number of extended gapless excitations as aclean Fermi-liquid, the diffusive metal exhibits only boundary-law entanglementscaling. This result pinpoints the sharp Fermi-surface structure, rather thanthe finite density of gapless excitations, as the origin of the log-correctionin the Fermi-liquid entanglement scaling.

Boundary-law scaling of entanglement entropy in diffusive metals