Collective neutrino oscillations with tensor networks using a time-dependent variational principle

TL;DR

This paper explores the use of tensor network methods combined with a time-dependent variational principle to simulate the complex many-body dynamics of dense neutrino systems, surpassing traditional computational limits.

Contribution

It introduces a novel tensor network approach with error measures for large-N neutrino flavor evolution beyond mean-field approximations.

Findings

Tensor network methods effectively simulate large neutrino systems.

New error measures based on conserved charges validate the simulations.

The approach captures beyond-mean-field correlations in neutrino oscillations.

Abstract

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.