Based on the quantum renormalization group, we derive the bulk geometry that
emerges in the holographic dual of the fermionic U(N) vector model at a nonzero
charge density. The obstruction that prohibits the metallic state from being
smoothly deformable to the direct product state under the renormalization group
flow gives rise to a horizon at a finite radial coordinate in the bulk. The
region outside the horizon is described by the Lifshitz geometry with a
higher-spin hair determined by microscopic details of the boundary theory. On
the other hand, the interior of the horizon is not described by any Riemannian
manifold, as it exhibits an algebraic non-locality. The non-local structure
inside the horizon carries the information on the shape of the filled Fermi
sea.