Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets

It is conjectured that the Haldane phase of the $S=1\mathrm{}$ antiferromagnetic Heisenberg chain and the $S=1\mathrm{}/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain is stable against any strength of randomness, because of imposed breakdown of translational symmetry. This conjecture is confirmed by the density matrix renormalization group calculation of the string order parameter and the energy gap distribution.