The quantum lattice gas model is used for investigation of low-frequency dynamics of the one-dimensional lattice (an analogue of the H-bonded atomic chain) with the two minima local anharmonic potential. Short-range correlations and particle hopping within potential wells as well as between of them are taken into account. The dynamical dipole susceptibility that determines the dielectric response of the system, is calculated using the exact diagonalization procedure on clasters and the Green's function formalism. The density of vibrational states is found, its frequency dependence is analyzed. The splitting of the lowest branch in spectrum in the region of transition to the ordered ground state (instead of the standard soft-mode behaviour) is revealed.
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