  The aim of this series of two papers is to discuss topological invariants for
interacting topological insulators (TIs). In the first paper (I), we provide a
paradigm of efficient numerical evaluation scheme for topological invariants,
in which we demystify the procedures and techniques employed in calculating Z2
invariant and spin Chern number via zero-frequency single-particle Green's
function in quantum Monte Carlo (QMC) simulations. Here we introduce a
periodization process to overcome the ubiquitous finite-size effect, so that
the calculated spin Chern number shows ideally quantized values. We also show
that making use of symmetry properties of the underlying systems can greatly
reduce the computational effort. To demonstrate the effectiveness of our
numerical evaluation scheme, especially the periodization process, of
topological invariants, we apply it on two independent two-dimensional models
of interacting topological insulators. In the subsequent paper (II), we apply
the scheme developed here to wider classes of models of interacting topological
insulators, for which certain limitation of constructing topological invariant
via single-particle Green's functions will be presented.
