Holographic Entanglement Entropy of Semi-local Quantum Liquids

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) x 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. 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.