20-07E

The equilibrium states of one-dimensional proton conductors in the systems with hydrogen bonds are investigated. Our extended hard-core boson lattice model includes short-range interactions between protons, their transfer along hydrogen bonds with the two-minima local anharmonic potential as well as their inter-bond hopping, and the modulating field is taken into account. The exact diagonalization method for finite one-dimensional system with periodic boundary conditions was used. The  existence of various phases of the system at T = 0, depending on the values of short-range interactions between particles and the modulating field strength, was established by analyzing the character of the obtained frequency dependence of one-particle spectral density.