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The devil's staircase is a fractal structure that characterizes the groundstate of one-dimensional classical lattice gases with long-range repulsiveconvex interactions. Its plateaus mark regions of stability for specificfilling fractions which are controlled by a chemical potential. Typically suchstaircase has an explicit particle-hole symmetry, i.e., the staircase at morethan half-filling can be trivially extracted from the one at less than halffilling by exchanging the roles of holes and particles. Here we introduce aquantum spin chain with competing short-range attractive and long-rangerepulsive interactions, i.e. a non-convex potential. In the classical limit theground state features generalized Wigner crystals that --- depending on thefilling fraction --- are either composed of dimer particles or dimer holeswhich results in an emergent complete devil's staircase without explicitparticle-hole symmetry of the underlying microscopic model. In our system theparticle-hole symmetry is lifted due to the fact that the staircase iscontrolled through a two-body interaction rather than a one-body chemicalpotential. The introduction of quantum fluctuations through a transverse fieldmelts the staircase and ultimately makes the system enter a paramagnetic phase.For intermediate transverse field strengths, however, we identify a region,where the density-density correlations suggest the emergence of quasilong-range order. We discuss how this physics can be explored withRydberg-dressed atoms held in a lattice.

Emergent devil's staircase without particle-hole symmetry in Rydberg quantum gases with competing attractive and repulsive interactions