  If a system of flavor-oscillating neutrinos is at high enough densities that
neutrino-neutrino coherent forward scatterings are non-negligible, the system
becomes a time-dependent many-body problem. An important and open question is
whether the flavor evolution is sufficiently described by a mean-field approach
or can be strongly affected by correlations arising from two-body interactions
in the neutrino Hamiltonian, as measured by nontrivial quantum entanglement.
Numerical computations of the time evolution of many-body quantum systems are
challenging because the size of the Hilbert space scales exponentially with the
number of particles N in the system. Thus, it is important to investigate
approximate but beyond-mean-field numerical treatments at larger values of N.
Here we investigate the efficacy of tensor network methods to calculate the
time evolution of interacting neutrinos at larger values of N than are possible
with conventional methods. In particular, we introduce the use of
time-dependent variational principle methods to address the long-range (in
momentum space) interactions of the neutrino Hamiltonian when including many
distinct vacuum oscillation frequencies. We also define new error measures
based upon the instantaneously conserved charge operators known for this
Hamiltonian to determine validity of large-N tensor network calculations.
