In  Kenneth G. Wilson proposed a mechanism for confinement using lattice paths what leds him to the concept of Wilson loop. It seems to me that he is using mainly a single abelian field. He says
The model discussed in this paper is a single Abelian gauge field coupled (with strength g) to massive quarks. In weak coupling the gauge field behaves like a normal free zero-mass field (despite modifications introduced in the lattice quantization) and the quarks are unbound. In strong coupling the gauge field is massive and the quarks are bound, showing the existence of the second phase
Despite he never uses the word "QED" I think that his model would show that there is a confining phase in QED at strong coupling. But it is not clear to me if the potential between sources in an abelian gauge field theory must be always a Coulomb type.
From my knowledge what we want is a theory describing the confinement and deconfined phases, at least for QCD, or not?
Is the mechanism proposed by Wilson predicting that QED has a confining phase?
 Kenneth G. Wilson; Confinement of Quarks; Phys.Rev. D10 (1974) 2445-2459