Ergodic Archimedean dimers

We study perfect matchings, or close-packed dimer coverings, of finite sections the eleven Archimedean lattices and give a constructive proof showing that any two matchings can be transformed into each other using small sets local ring-exchange moves. This result has direct consequences for formulating quantum models with resonating valence bond ground state, i.e., superposition all coverings compatible boundary conditions. On five composite we supplement sufficiency translationally invariant reference configurations prove strict necessity sufficient terms respect to ergodicity. provide examples discuss frustration-free deformations on tripartite lattices.