  We implement and characterize a numerical algorithm inspired by the
$s$-source framework [Phys. Rev.~B 93, 045127 (2016)] for building a quantum
many-body ground state wavefunction on a lattice of size $2L$ by applying
adiabatic evolution to the corresponding ground state at size $L$, along with
$L$ interleaved ancillae. The procedure can in principle be iterated to
repeatedly double the size of the system. We implement the algorithm for
several one dimensional spin model Hamiltonians, and find that the construction
works particularly well when the gap is large and, interestingly, at scale
invariant critical points. We explain this feature as a natural consequence of
the lattice expansion procedure. This behavior holds for both the integrable
transverse-field Ising model and non-integrable variations. We also develop an
analytic perturbative understanding of the errors deep in either phase of the
transverse field Ising model, and suggest how the circuit could be modified to
parametrically reduce errors. In addition to sharpening our perspective on
entanglement renormalization in 1D, the algorithm could also potentially be
used to build states experimentally, enabling the realization of certain
long-range correlated states with low depth quantum circuits.
