  A systematic method for determining order parameters for quantum many-body
systems on lattices is developed by utilizing reduced density matrices. This
method allows one to extract the order parameter directly from the wave
functions of the degenerate ground states without aid of empirical knowledge,
and thus opens a way to explore unknown exotic orders. The applicability of
this method is demonstrated numerically or rigorously in models which are
considered to exhibit dimer, scalar chiral, and topological orders.
