S = 1/2 QUANTUM HEISENBERG LADDER AND S = 1 HALDANE PHASE

We investigate an S=(1/2) ladder model with a ferromagnetic interchain coupling (-lambda) and an antiferromagnetic intrachain coupling based on the bosonization method, which reduces to the S=1 antiferromagnetic Heisenberg model in the limit lambda-->infinity. We argue with the aid of Wilson's renormalization group method that the ground state is the Haldane state with an excitation gap for lambda>0, that the gap opens at lambda=0 exponentially and that the critical index of the coherence length is unity (nu=1) on the critical line between the antiferromagnetic and the Haldane phases. Furthermore, it is found that the string order parameter proposed by den Nijs and Rommelse is expressed by a local order parameter in the bosonization method.