  We present a new exact renormalization approach for quantum lattice models
leading to long-range interactions. The renormalization scheme is based on
wavelets with an infinite support in such a way that the excitation spectrum at
the fixed point coincides with the spectrum of the associated short-range
continuum model in an energy range below an upper cutoff imposed by the lattice
spacing. As a consequence, the conformal towers of spectrum are exactly
realized on the lattice up to a certain energy scale. We exemplify our approach
by applying it to free bosons and to free fermions in $1+1$ dimensions, as well
as to the Ising model. The analysis is also motivated by tensor network
approaches to the AdS/CFT correspondence since our results may be useful for a
qualitatively new construction of holographic duals complementary to previous
approaches based on finite-range wavelets.
