Haldane energy gap of a doped linear-chain Heisenberg antiferromagnet.

Using the valence-bond-solid (VBS) approach and the Schwinger boson mean field approximation, we study the dependence of the Haldane gap of a spin-1 linear chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter ∆ and the constraint factor λ. As a result, the Haldane gap is reduced by a factor ∼ n 2/3 i , with ni as the impurity concentration, and eventually collapses at ni ∼ 1/ξ with ξ as the VBS correlation length. This theoretical prediction can be verified by neutron scattering experiments.