Compact quantum electrodynamics in 2+1 dimensions and spinon deconfinement: a renormalization group analysis

We discuss compact (2+1)-dimensional Maxwell electrodynamics coupled to fermionic matter with N replica. For large enough N, the latter corresponds to an effective theory for the nearest neighbor SU(N) Heisenberg antiferromagnet, in which the fermions represent solitonic excitations known as spinons. Here we show that the spinons are deconfined for $N>N_c=36$, thus leading to an insulating state known as spin liquid. A previous analysis considerably underestimated the value of $N_c$. We show further that for $20<N\leq 36$ there can be either a confined or a deconfined phase, depending on the instanton density. For $N\leq 20$ only the confined phase exist. For the physically relevant value N=2 we argue that no paramagnetic phase can emerge, since chiral symmetry breaking would disrupt it. In such a case a spin liquid or any other nontrivial paramagnetic state (for instance, a valence-bond solid) is only possible if doping or frustrating interactions are included.