  We propose a lattice model of supersymmetric complex quantum mechanics which
realizes the non-renormalization theorem on a lattice. In our lattice model,
the Leibniz rule in the continuum, which cannot hold on a lattice due to a
no-go theorem, is replaced by the cyclic Leibniz rule (CLR) for difference
operators. It is shown that CLR allows two of four supercharges of the
continuum theory to preserve while a naive lattice model can realize one
supercharge at the most. A striking feature of our lattice model is that there
are no quantum corrections to potential terms in any finite order of
perturbation theory. This is one of characteristic properties of supersymmetric
theories in the continuum. It turns out that CLR plays a crucial role in the
proof of the non-renormalization theorem. This result suggests that CLR grasps
an essence of supersymmetry on a lattice.
