Topological effects in short antiferromagnetic Heisenberg chains

The manifestations of topological effects in finite antiferromagnetic Heisenberg chains are examined by density-matrix renormalization-group techniques. We find that the difference between integer and half-integer spin chains shows up in ground-state energy per site when the length of the spin chain is longer than ~ξ, where ξ~exp(πS) is a spin-spin correlation length, for spin magnitudes S up to 5/2. For open chains with spin magnitudes S=5/2 to S=5, we verify that end states with fractional spin quantum numbers S' exist and are visible in the structure of the low-energy excitation spectrum even when the chain length is much smaller than the correlation length ξ. The robustness of end states points to the possibility of the existence of general hidden topological order in quantum spin chains with spin magnitudes S>=1.