  We construct a two-dimensional microscopic model of interacting quantum
dimers that displays an infinite number of periodic striped phases in its T=0
phase diagram. The phases form an incomplete devil's staircase and the period
becomes arbitrarily large as the staircase is traversed. The Hamiltonian has
purely short-range interactions, does not break any symmetries of the
underlying square lattice, and is generic in that it does not involve the
fine-tuning of a large number of parameters. Our model, a quantum mechanical
analog of the Pokrovsky-Talapov model of fluctuating domain walls in two
dimensional classical statistical mechanics, provides a mechanism by which
striped phases with periods large compared to the lattice spacing can, in
principle, form in frustrated quantum magnetic systems with only short-ranged
interactions and no explicitly broken symmetries.
