Statistical properties of spectra of the Heisenberg Hamiltonian

Spectra of several types of finite Heisenberg lattices have been studied us ing methods of statistical spectroscopy. In particular, spectral density di stributions, discrete spectra generated from the spectral density distribut ion moments, and the distributions of spacings between the neighboring ener gy levels have been analyzed. The densities have been shown to be nearly Ga ussian and the spectra generated from their several-moment Gram-Charlier ap proximations are in a good agreement with the exact ones, except for severa l extreme energy levels. Spacings between the neighboring levels exhibit cl ustering of the energy levels stronger than that given by the Poisson distr ibution, showing an essential influence of the point-group symmetries of th e lattices. [S0163-1829(99)11303-1].