Exactly solvable Dimer Liquid and Ising Gauge Theory of a nonplanar Quantum 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. This fully integrable model realizes a fully gapped and disordered dimer liquid phase with topological degeneracy and deconfined fractional excitations. Results concerning the entanglement behavior and the identification of ground states with minimum entanglement entropy, which reflect the quasiparticle excitations of the topological phase, are obtained. Additionally we elaborate on an exact mapping to Z₂ lattice gauge theory previously only investigated in the context of planar dimer models.