Quantum Phase Transition in One-Dimensional Commensurate Frenkel-Kontorova Model

We have studied the one-dimensional commensurate quantum Frenkel-Kontorova model by using a density-matrix renormalization group (DMRG) algorithm. The focus has been on its properties of entanglement, coordinate correlation, ground-state energy and energy gap between the ground state and the first excited state. It is demonstrated that a quantum phase transition (QPT) between the pinned and the sliding phases takes place as the quantum fluctuation, measured on the basis of an effective Planck constant (h) over tilde, increases to a threshold value (h) over tilde (c).