Exact diagonalisations of open spin-1 chains

The author numerically computes the two lowest eigenvalues of finite length spin-1 chains with the Hamiltonian H= Sigma _i(S_i.S _i+1- beta (S_i.S_i+1)²) and open boundary conditions. For a range of beta , including the value 0, he finds that the difference of the two eigenvalues decays exponentially with the length of the chain. This exponential decay provides further evidence that these spin chains are in a massive phase as first predicted by Haldane (1982). The correlation length xi of the chain can be estimated using this exponential decay. He finds estimates of xi for the Heisenberg chain ( beta =0) that range from 6.7 to 7.8 depending on how one extrapolates to infinite length.