By using the density-matrix renormalization group technique, the incommensurate quantum Frenkel-Kontorova model is investigated numerically. It is found that when the quantum fluctuation is strong enough, the
g function featured by a sawtooth map in the depinned state will show a different kind of behavior, similar to a standard map, but with reduced magnitude. The related position correlations are studied in detail, which leads to a potentially interesting application to the recently well-explored phase transitions in cold atoms loaded in optical lattices.
In this paper, the one-dimensional incommensurate quantum Frenkel-Kontorova model is investigate by a density-matrix renormalization group algorithm. Special attention is given to the entanglement and the ground state energy. The energy gap between the ground state and the first excited is also calculated. From all the numerical results, we have observed an obvious property changes from the pinned state to the sliding one as the quantum fluctuation is increased. But no expected quantum critical point can be justified by the present data.