We introduce a general framework to construct many-body lattice wavefunctions
starting from the conformal blocks (CBs) of rational conformal field theories
(RCFTs). We discuss the different ways of encoding the physical degrees of
freedom of the lattice system using both the internal symmetries of the theory
and the fusion channels of the CBs. We illustrate this construction both by
revisiting the known Haldane-Shastry model and by providing a novel
implementation for the Ising RCFT. In the latter case, we find a connection to
the Ising transverse field (ITF) spin chain via the Kramers-Wannier duality and
the Temperley-Lieb-Jones algebra. We also find evidence that the ground state
of the finite-size critical ITF Hamiltonian corresponds exactly to the
wavefunction obtained from CBs of spin fields