Entanglement in two- and three-flavor collective neutrino oscillations

The evolution of collective neutrino flavor oscillations that arises when the neutrinos are at high densities is a time-dependent quantum many-body problem. Solving such a problem is computationally complex in the sense that the size of the Hilbert space increases exponentially with the increase in the number of particles. One possibility to simplify this problem is solving it in the mean-field approximation. However, such an approximation does not consider the correlations between neutrinos resulting from the two-body interactions. Therefore, it is worth exploring the other numerical approaches to solve the quantum many-body problem within some approximation but still encountering the beyond-mean-field effects. The tensor network methods are a powerful tool in that direction. We employ one of the tensor network methods, the time-dependent variational principle method, to solve the time-dependent neutrino many-body problem. The superiority of the tensor network methods over the conventional methods like Runge-Kutta and Lanczos to investigate the collective neutrino oscillations when the number of neutrinos increases will be discussed in this talk.

The entanglement in three-flavor settings has never been explored in the many-body picture. Several exciting features have been observed in the mean-field calculations of the three-flavor case. Our study found that neutrinos are more entangled when considering all three flavors in the many-body picture. This talk will also discuss the results of the many-body treatment of three-flavor collective neutrino oscillations.