Quantum phase transition in the random antiferromagnetic spin-1 chain

We study the random antiferromagnetic spin-1 chain following the evolution of the bond probability distributions under a renormalization group transformation. We use a mapping of the spin-1 chain into an effective spin-1/2 chain with both ferromagnetic (odd bonds) and antiferromagnetic (even and odd bonds) interactions. We obtain a recursion relation for the coupling constants, solving exactly up to a four-spin cluster. Our improved perturbation treatment on these larger clusters shows that the random singlet phase in the spin-1 chain, differently from previous results, is obtained only when 100% of the odd bonds are strong ferromagnetic, i.e., larger than the even antiferromagnetic bonds. Otherwise the ground state is that of a dimerized spin-1/2 chain.