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We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation. Surprisingly we find patterns reminiscent of more orderly interactions, such as a predominance of J0ex{0ex}=0ex{0ex}0 ground states separated by a gap from the excited states, and evidence of phonon vibrations in the low-lying spectra.
Johnson et al. (Mon,) studied this question.
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