Devil's staircase in a quantum dimer model on the hexagonal lattice

Quantum dimer models appear in different contexts when describing dynamics in constrained low-energy manifolds, such as for frustrated Ising models in weak transverse fields. In this talk, I address a particularly interesting case, where a quantum dimer model on the hexagonal lattice, in addition to the standard Rokhsar-Kivelson Hamiltonian, includes a competing potential term, counting dimer-free hexagons. It has a rich zero-temperature phase diagram that comprises a cascade of rapidly changing flux quantum numbers (tilt in the height language). This cascade is partially of fractal nature and the model provides, in particular, a microscopic realization of the ``devil's staircase'' scenario [E.\ Fradkin {\it et al.} Phys. Rev. B {\bf 69}, 224415 (2004)]. We have studied the system by means of quantum Monte-Carlo simulations and the results can be explained using perturbation theory, RG, and variational arguments.\\ References: arXiv:1507.04643, arXiv:1501.02242.