Quantum three-coloring dimer model and the disruptive effect of quantum glassiness on its line of critical points

We construct a quantum extension of the (classical) three-coloring model introduced by Baxter [J.Math.Phys.11, 784 (1970)] for which the ground state can be computed exactly along a continuous line of Rokhsar-Kivelson solvable points. The quantum model, which admits a local spin representation, displays at least three different phases; an antiferromagnetic (AF) phase, a line of quantum critical points, and a ferromagnetic (F) phase. We argue that, in the ferromagnetic phase, the system cannot reach dynamically the quantum ground state when coupled to a bath through local interactions, and thus lingers in a state of quantum glassiness.