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

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. © 1980 The American Physical Society.