Topological effects at short antiferromagnetic Heisenberg chains

The manifestations of topological effects in finite antiferromagnetic Heisenberg chains is examined by density matrix renormalization group technique in this paper. We find that difference between integer and half-integer spin chains shows up in ground state energy per site when length of spin chain is longer than $\sim \xi$, where $\xi \sim \exp (\pi S)$ is a spin-spin correlation length, for spin magnitude S up to 5/2. For open chains with spin magnitudes $S=5\mathrm{/}2$ to S=5, we verify that end states with fractional spin quantum numbers $S^{\mathrm{\prime }}$ exist and are visible even when the chain length is much smaller than the correlation length $\xi$. The end states manifest themselves in the structure of the low energy excitation spectrum.