Application of the t-adaptive density matrix renormalization group method to the quantum Frenkel-Kontorova model

In this paper, the t-adaptive density matrix renormalization group method has been applied to study the dynamics of the one-dimensional quantum Frenkel-Kontorova model. It is found that as the quantum fluctuations increase, the local excitations will become unstable. The unstableness will lead to the dominance of the phonon excitations as the elementary excitations of the system in the deep quantum regime.