Exact solution and correlations of a dimer model on the checkerboard lattice

We present analytic results for a special dimer model on the nonbipartite and nonplanar checkerboard lattice that does not allow for parallel dimers surrounding diagonal links. We exactly calculate the number of closed packed dimer coverings on finite checkerboard lattices under periodic boundary conditions and determine all dimer-dimer correlations. The latter are found to vanish beyond a certain distance. We find that this solvable model, despite being nonplanar, is in close kinship with well-known paradigm-setting planar counterparts that allow exact mappings to Z2 lattice gauge theory.