  We consider the holographic entanglement entropy of $(d+2)$-dimensional
semi-local quantum liquids, for which the dual gravity background in the deep
interior is $AdS_{2}\times\mathbb{R}^{d}$ multiplied by a warp factor which
depends on the radial coordinate. The entropy density of this geometry goes to
zero in the extremal limit. The thermodynamics associated with this semi-local
background is discussed via dimensional analysis and scaling arguments. For the
case of an asymptotically AdS UV completion of this geometry, we show that the
entanglement entropy of a strip and an annulus exhibits a phase transition as a
typical length of the different shapes is varied, while there is no sign of
such a transition for the entanglement entropy of a sphere. Moreover, for the
spherical entangling region, the leading order contribution to the entanglement
entropy in the IR is calculated analytically. It exhibits an area law behaviour
and agrees with the numerical result.
