  An exact solvable 'zig-zag' ladder model of degenerated spinless fermions is
proposed and solved exactly by the means of the Bethe ansatz. An effective
attractive hard-core interaction and direct Coulomb repulsion of fermions on
the nearest-neighbor sites of different chains induce a new phase state of the
ladder. We give a detailed analysis of the exact phase diagram at zero
temperature, that is characterized by two phases at the filling exceeding 2/3:
itinerant and 'frozen' fermions, for which two different species reside in
spatially separate regions. The critical exponents describing asymptotic
behavior of the correlation functions are calculated using the Bethe ansatz and
conformal field theory. It is shown also, that the density of the magnetization
of the corresponding zig-zag spin-1/2 ladder has a jump equal to 1/3 at the
magnetic field equal to zero.
