Destruction of "the devil's staircase" by quantum fluctuations

Abstract
The quantum ground state of a linear chain of atoms in a periodic potential is studied. Classically, the average periodicity of the lattice locks into an infinity of commensurate values as the parameters are varied. It is shown that this "devil's staircase" behavior does not survive quantum fluctuations; only a finite number of commensurate phases are stable at zero temperature. In between the periodicity is generally incommensurate.