Edge states in open antiferromagnetic Heisenberg chains

We report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes S=1/2,1,3/2,2 using the density-matrix renormalization-group method initiated by White. For integer spin chains, we find that edge states with spin magnitude ${\mathit{S}}_{\mathrm{edge}}$=S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a ${\mathit{S}}_{\mathrm{edge}}$=1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.