  Systems of strongly correlated fermions on certain geometrically frustrated
lattices at particular filling factors support excitations with fractional
charges $\pm e/2$. We calculate quantum mechanical ground states, low--lying
excitations and spectral functions of finite lattices by means of numerical
diagonalization. The ground state of the most thoroughfully studied case, the
criss-crossed checkerboard lattice, is degenerate and shows long--range order.
Static fractional charges are confined by a weak linear force, most probably
leading to bound states of large spatial extent. Consequently, the
quasi-particle weight is reduced, which reflects the internal dynamics of the
fractionally charged excitations. By using an additional parameter, we
fine--tune the system to a special point at which fractional charges are
manifestly deconfined--the so--called Rokhsar--Kivelson point. For a deeper
understanding of the low--energy physics of these models and for numerical
advantages, several conserved quantum numbers are identified.
