Study on the quantum FK model

In this paper, we present a variational method which is suitable for invest igating the quantum Frenkel-Kontorova model. For the cases of using the coh erent state and the squeezed state as the trial wave functions of the groun d 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 eff ective potential method, determine the critical points K-c for different I using Greene's criterion. The results given in the present paper are qualit atively consistent with those of the numerical experiments.([6])