Exact ground state for 1D electronic models

We have found the exact ground state for two electronic models on a linear chain. The first model describes half-filling electron system in the ferromagnet–antiferromagnet transition point. In the singlet ground state the spin correlators show giant spiral magnetic ordering with the period of a spiral equals to the system size. The second electronic model describes the point where the ground state has giant spiral off-diagonal long-range order and, therefore, superconducting. We suggest the formation of the ground state with giant spiral order (ferromagnetic or off-diagonal) as a probable scenario of the subsequent destruction of the ferromagnetism and the superconductivity.