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The decades-long search for a shape that tiles the plane only aperiodicallyunder translations and rotations recently ended with the discovery of the`spectre' aperiodic monotile. In this setting we study the dimer model, inwhich dimers are placed along tile edges such that each vertex meets preciselyone dimer. The complexity of the tiling combines with the dimer constraint toallow an exact solution to the model. The partition function is$\mathcal{Z}=2^{N_{\textrm{Mystic}}+1}$ where $N_{\textrm{Mystic}}$ is thenumber of `Mystic' tiles. We exactly solve the quantum dimer (Rokhsar Kivelson)model in the same setting by identifying an eigenbasis at all interactionstrengths $V/t$. We find that test monomers, once created, can be infinitelyseparated at zero energy cost for all $V/t$, constituting a deconfined phase ina 2+1D bipartite quantum dimer model.

Exact Solution to the Quantum and Classical Dimer Models on the Spectre Aperiodic Monotiling