07-21U

We investigate the energy spectrum of finate one-dimensional chains with proton (ionic) conductivity described by fermionic lattice modles. Using exact diagonalization technique we calculate the density of states for the chains of up to 10 sites. At half-filling for the case of weak correlation the spectra consists of one band and therefore the system is in the quasi-metallic state. When the correlation become strong enough the spectra develops the gap and the system becomes an insulator. At certain values of parameters we observe metal-insulator like transition with the change of tempetarure. The results obtained numerically are compared to the ones obtained previously with different analytical approaches.