  A formula for the corner charge in terms of the bulk quadrupole moment is
derived for two-dimensional periodic systems. This is an analog of the formula
for the surface charge density in terms of the bulk polarization. In the
presence of an $n$-fold rotation symmetry with $n=3$, $4$, and $6$, the
quadrupole moment is quantized and is independent of the spread or shape of
Wannier orbitals, depending only on the location of Wannier centers of filled
bands. In this case, our formula predicts the fractional part of the quadrupole
moment purely from the bulk property. The system can contain many-body
interactions as long as the ground state is gapped and topologically trivial in
the sense it is smoothly connected to a product state limit. An extension of
these results to three-dimensional systems is also discussed. In three
dimensions, in general, even the fractional part of the corner charge is not
fully predictable from the bulk perspective even in the presence of point group
symmetry.
