Numerical analysis of the bond-random antiferromagnetic S=1 Heisenberg chain

The ground state of the bond-random antiferromagnetic S=1 Heisenberg chain with the biquadratic interaction -β∑ _i( S_i·S_i+1) ² is investigated by means of the exact-diagonalization method and the finite-size-scaling analysis. It is shown that the Haldane phase β≈0 persists against the randomness; namely, no randomness-driven phase transition is observed until at a point of extremely broad-bond distribution. We found that in the Haldane phase, the magnetic correlation length is kept hardly changed. These results are contrastive to those of an analytic theory which predicts a second-order phase transition between the Haldane and the random-singlet phases at a certain critical randomness.