ON THE PHYSICAL SIGNIFICANCE OF THE HIGH-DIMENSIONAL BETHE-ANSATZ

A trial wave-function, consisting of a linear combination of many-magn on plane waves, all characterized by the same sequence of momenta, is shown to be an eigenstate of the two-dimensional Heisenberg Hamiltonia n. The partial waves are related together via interaction and momentum -dependent scattering amplitudes. Each of them reflects a sequence of two-body scattering events, during which both involved particles excha nge their respective momentum along one direction of space only. The c orresponding eigenvalue is obtained as a sum over one-magnon energies. These results generalize those obtained with the help of the Bethe an satz to arbitrary dimension. However, unlike the one-dimensional case, these eigenstates do not build a complete set in dimension, >1. (C) 1 998 Elsevier Science B.V. All rights reserved.