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 , increases to a threshold value h_c. 2014 The Physical Society of Japan.