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The 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 $Δ$ and the constraint factor $λ$. As a result, the Haldane gap is reduced by a factor $ \sim n_i^{2/3}$, with $n_i$ as the impurity concentration, and eventually collapses at $n_i \sim 1/ξ$ with $ξ$ as the VBS correlation length. This theoretical prediction can be verified by neutron scattering experiments.