  Implementing the Wilsonian renormalization group (RG) transformation in a
nonperturbative way, we construct an effective holographic dual description
with an emergent extradimension identified with an RG scale. Taking the
large$-N$ limit, we obtain an equation of motion of an order-parameter field,
here the chiral condensate for our explicit demonstration. In particular, an
intertwined structure manifests between the first-order RG flow equations of
renormalized coupling functions and the second-order differential equation of
the order-parameter field, thus referred to as a nonperturbative RG-improved
mean-field theory. Assuming translational symmetry as a vacuum state, we solve
these nonlinear coupled mean-field equations based on a matching method between
UV- and IR-regional solutions. As a result, we find an RG flow from a
weakly-coupled chiral-symmetric UV fixed point to a strongly-correlated
chiral-symmetry broken IR fixed point, where the renormalized velocity of Dirac
fermions vanishes most rapidly and effective quantum mechanics appears at IR.
Furthermore, we translate these RG flows of coupling functions into those of
emergent metric tensors and extract out geometrical properties of the emergent
holographic spacetime constructed from the UV- and IR-regional solutions.
Surprisingly, we obtain the volume law of entanglement entropy in the
Ryu-Takayanagi formula, which implies appearance of a black hole type solution
in the limit of infinite cutoff even at zero temperature. We critically discuss
our field theoretic interpretation for this solution in terms of potentially
gapless multi-particle excitation spectra.
