SU (N) antiferromagnets and the phase structure of QED in the strong coupling limit

We examine the strong coupling limit of both compact and non-compact quantum electrodynamics (QED) on a lattice with staggered fermions. We show that every SU (N(L)) quantum antiferromagnet with spins in a particular fundamental representation of the SU (N(L)) Lie algebra and with nearest neighbor couplings on a bipartite lattice is exactly equivalent to the infinite coupling limit of lattice QED with the number of flavors of electrons related to N(L) and the dimension of space-time, D + 1. We find that, for both compact and non-compact QED, when N(L) is odd the ground state of the strong coupling limit breaks chiral symmetry in any dimensions and for any N(L) and the condensate is an isoscalar mass operator. When N(L) is even, chiral symmetry is broken if D greater-than-or-equal-to 2 and if N(L) is small enough; in this case the order parameter is an isovector mass operator. We also find the exact ground state of the lattice Coulomb gas as well as a variety of related lattice statistical systems with long-range interactions.