  We apply the quantum renormalization group to construct a holographic dual
for the U(N) vector model for complex bosons defined on a lattice. The bulk
geometry becomes dynamical as the hopping amplitudes which determine
connectivity of space are promoted to quantum variables. In the large N limit,
the full bulk equations of motion for the dynamical hopping fields are
numerically solved for finite systems. From finite size scaling, we show that
different phases exhibit distinct geometric features in the bulk. In the
insulating phase, the space gets fragmented into isolated islands deep inside
the bulk, exhibiting ultra-locality. In the superfluid phase, the bulk exhibits
a horizon beyond which the geometry becomes non-local. Right at the horizon,
the hopping fields decay with a universal power-law in coordinate distance
between sites, while they decay in slower power-laws with continuously varying
exponents inside the horizon. At the critical point, the bulk exhibits a local
geometry whose characteristic length scale diverges asymptotically in the IR
limit.
