THE HALDANE-GAP IN ANTIFERROMAGNETIC HEISENBERG-CHAINS

Integer-spin Heisenberg antiferromagnetic chains are expected to have a singlet groundstate and a gap to the first excited state, as first argued by Haldane. We review rigorous results on this conjecture and discuss experimental realizations. Theoretical and experimental aspects of three recent developments in this field are then reviewed: chain-end excitations and the non-local order parameter, a field theory mapping and behavior near zero wave-vector, high-field behavior and one-dimensional Bose condensation.