Study on the Quantum FK Model

In this paper, we present a variational method which is suitable for investigating the quantum Frenkel-Kontorova model. For the cases of using the coherent state and the squeezed state as the trial wave functions of the ground states, the quantum Hamiltonians and the quantum maps are given. For the second case, rye present the phase diagram and devil's stairs using the effective potential method, determine the critical points K-c for different I using Greene's criterion. The results given in the present paper are qualitatively consistent with those of the numerical experiments.([6])