Exactly solvable 1D frustrated quantum spin models

A class of the frustrated quantum s = 1/2 models with nearest and next nearest neighbor couplings is investigated. An exact wave function of the singlet ground state at the transition point from the ferromagnetic to the singlet state is presented. The recurrence technics of expectation value calculations is developed and the simple expressions for spin-correlation function at N --> infinity are obtained. A long range double-spiral ordering is demonstrated. We show that in one particular case the model reduces to the effective spin-1 model and the exact singlet ground state wave function is presented for this model. The behavior of the system in the vicinity of the transition point is investigated.