Square kagome quantum antiferromagnet and the eight-vertex model

We introduce a two-dimensional network of corner-sharing triangles with square-lattice symmetry. Properties of magnetic systems here should be similar to those on a kagome lattice. Focusing on the spin-1/2 Heisenberg quantum antiferromagnet, we generalize die spin symmetry group from SU(2) to SU(N). In the large-N limit, we map the model exactly to the eight-vertex model solved by Baxter. We predict an exponential number of low-lying singlet states, a triplet gap, and a two-peak specific heat. In addition, the large-N limit suggests a finite temperature phase transition into a phase with ordered resonance loop and broken translational symmetry.