  Incompressible insulating phases of electronic systems at partial filling of
a lattice are often associated with charge ordering that breaks lattice
symmetry. The resulting phases have an enlarged unit cell with an effective
integer filling. Here we explore the possibility of insulating states - which
we dub "Quantum Charge Liquids" (QCL) - at partial lattice filling that
preserve lattice translation symmetry. Such QCL phases must necessarily either
have gapped fractionally charged excitations and associated topological order
or have gapless neutral excitations. We establish some general constraints on
gapped fermionic QCL phases that restrict the nature of their topological
order. We prove a number of results on the minimal topological order that is
consistent with the lattice filling. In particular we show that at rational
fillings $\nu = p/q$ with $q$ an even integer the minimal ground state
degeneracy on a torus of the fermionic QCL is $4q^2$, 4 times larger than that
of the bosonic QCL at the same filling. We comment on models and physical
systems which may host fermionic QCL phases and discuss the phenomenology of
these phases.
