  We provide a rigorous lattice approximation of conformal field theories given
in terms of lattice fermions in 1+1-dimensions, focussing on free fermion
models and Wess-Zumino-Witten models. To this end, we utilize a recently
introduced operator-algebraic framework for Wilson-Kadanoff renormalization. In
this setting, we prove the convergence of the approximation of the Virasoro
generators by the Koo-Saleur formula. From this, we deduce the convergence of
lattice approximations of conformal correlation functions to their continuum
limit. In addition, we show how these results lead to explicit error estimates
pertaining to the quantum simulation of conformal field theories.
