The structure of the ground state of the quantum discrete Frenkel-Kontorova model was numerically analyzed by means of the Metropolis algorithm in [38,41]. Special attention was given to the effects of quantization on the Cantori structure of the classical ground state. It was shown that these quantum effects produce a new structure which is described by using a sawtooth map instead of the Chirikov standard map. At sufficiently large values of the Cantori is destroyed. These results formed the basis of thesis of F.Borgonovi (Pavia Univ., 1990).