  Topological or deconfined phases of matter exhibit emergent gauge fields and
quasiparticles that carry a corresponding gauge charge. In systems with an
intrinsic conserved U(1) charge, such as all electronic systems where the
Coulombic charge plays this role, these quasiparticles are also characterized
by their intrinsic charge. We show that one can take advantage of the
topological order fairly generally to produce periodic Hamiltonians which endow
the quasiparticles with continuously variable, generically irrational,
intrinsic charges. Examples include various topologically ordered lattice
models, the three dimensional RVB liquid on bipartite lattices as well as water
and spin ice. By contrast, the gauge charges of the quasiparticles retain their
quantized values.
