Mode-locking of incommensurate phase by quantum zero-point energy in the Frenkel-Kontorova model

In this paper, it is shown that a configuration-modulated system described by the Frenkel-Kontorova model can be locked at an incommensurate phase when the quantum zero-point energy is taken into account. It is also found that the specific heat for an incommensurate phase shows a different parameter dependence in the sliding phase and pinning phase. These findings provide a possible way for experimentalists to verify the phase transition by breaking of analyticity.