  We present a position operator that is compatible with periodic boundary
conditions (PBC). It is a one-body operator that can be applied in calculations
of correlated materials by simply replacing the traditional position vector by
the new definition. We show that it satisfies important fundamental as well as
practical constraints. To illustrate the usefulness of the PBC position
operator we apply it to the localization tensor, a key quantity that is able to
differentiate metallic from insulating states. In particular, we show that the
localization tensor given in terms of the PBC position operator yields the
correct expression in the thermodynamic limit. Moreover, we show that it
correctly distinguishes between finite precursors of metals and insulators.
