  The devil's staircase is a fractal structure that characterizes the ground
state of one-dimensional classical lattice gases with long-range repulsive
convex interactions. Its plateaus mark regions of stability for specific
filling fractions which are controlled by a chemical potential. Typically such
staircase has an explicit particle-hole symmetry, i.e., the staircase at more
than half-filling can be trivially extracted from the one at less than half
filling by exchanging the roles of holes and particles. Here we introduce a
quantum spin chain with competing short-range attractive and long-range
repulsive interactions, i.e. a non-convex potential. In the classical limit the
ground state features generalized Wigner crystals that --- depending on the
filling fraction --- are either composed of dimer particles or dimer holes
which results in an emergent complete devil's staircase without explicit
particle-hole symmetry of the underlying microscopic model. In our system the
particle-hole symmetry is lifted due to the fact that the staircase is
controlled through a two-body interaction rather than a one-body chemical
potential. The introduction of quantum fluctuations through a transverse field
melts 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 quasi
long-range order. We discuss how this physics can be explored with
Rydberg-dressed atoms held in a lattice.
