Abstract
We provide a route to constructing an electronic quantum charge liquid (QCL), a state made up of fermions at fractional filling of a lattice that does not break translation. Starting with spinless fermions at filling ν=3/2 we pair them to get bosons at filling ν=3/4 per unit cell. The tetramer model, a generalization of the dimer model, on the square lattice is evaluated as a candidate bosonic QCL at filling ν = 3/4. It is shown that these models exhibit a local Z₄ symmetry. Upon numerical study of a family of tetramer wavefunctions it is found that while one is gapless due to U(1)³ symmetry at least one other can be definitively shown to be gapped. The gapped nature of this state, along with its Z₄ symmetry, leads us to propose that it is an example of the elusive bosonic QCL displaying the minimal Z₄ topological order. We conclude by discussing possible extensions to other lattice geometries, electronic QCLs, and to Rydberg atoms.