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We study analytically and numerically the one-dimensional quantumFrenkel-Kontorova chain in the regime when the classical model is located inthe pinned phase characterized by the gaped phonon excitations and devil'sstaircase. By extensive quantum Monte Carlo simulations we show that for theeffective Planck constant $\hbar$ smaller than the critical value $\hbar_c$ thequantum chain is in the pinned instanton glass phase. In this phase theelementary excitations have two branches: phonons, separated from zero energyby a finite gap, and instantons which have an exponentially small excitationenergy. At $\hbar=\hbar_c$ the quantum phase transition takes place and for$\hbar>\hbar_c$ the pinned instanton glass is transformed into the slidingphonon gas with gapless phonon excitations. This transition is accompanied bythe divergence of the spatial correlation length and appearence of slidingmodes at $\hbar>\hbar_c$.Comment: revtex 16 pages, 18 figure

Quantum phase transition in the Frenkel-Kontorova chain: From pinned instanton glass to sliding phonon gas