  Collective neutrino oscillations are critical to determine the neutrino
flavor content, which has striking impacts on core-collapse supernovae or
compact binary merger remnants. It is a challenging many-body problem that so
far has been mainly studied at the mean-field approximation. We use a setup
that captures the relevant physics and allows exact solution for a large number
of neutrinos. We, for the first time, find quantitative deviation from the
mean-field evolution due to many-body decoherence in flavor space. Similar
features have been observed in a spin-1 Bose-Einstein condensate, which opens
the possibility of experimental explorations of collective flavor phenomena.
Our results call for more careful examinations on the possible many-body
corrections to collective neutrino oscillations in astrophysical environments.
