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

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.

19 pages, 9 figures

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• Basic Elements for Simulations of Standard Model Physics with Quantum Annealers: Multigrid and Clock States
• Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations
• Entanglement and correlations in fast collective neutrino flavor oscillations
• Role of non-gaussian quantum fluctuations in neutrino entanglement
• Entanglement in three-flavor collective neutrino oscillations
• Simulating neutrino oscillations on a superconducting qutrit
• Many-body collective neutrino oscillations: recent developments
• Inference finds consistency between a neutrino flavor evolution model and Earth-based solar neutrino measurements