J. Szeftel et al., ON THE PHYSICAL SIGNIFICANCE OF THE HIGH-DIMENSIONAL BETHE-ANSATZ, Journal of magnetism and magnetic materials, 187(2), 1998, pp. 261-267
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
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