Many-Body Simulations of the Fast Flavor Instability

Abstract

The neutrino fast flavor instability dominates the evolution of neutrino flavor within the engines of core-collapse supernovae and neutron star mergers. However, theoretical models of neutrino flavor change that include many-body quantum correlations can differ starkly from similar mean-field calculations. We demonstrate for the first time that the inhomogeneous fast flavor instability is disrupted by many-body correlations using a novel tensor network framework that allows a continuous transition between mean-field and many-body results by tuning the singular value decomposition cutoff value. Generalizing the forward-scattering Hamiltonian to spatially varying conditions, we demonstrate that the timescale of flavor transformation scales logarithmically with system size, suggesting that many-body effects could occur before mean-field instabilities are able to saturate. Our results have significant implications for astrophysical explosion dynamics, nucleosynthesis, and observable neutrino signatures.

Figures (5)

• Figure 1: Illustration of operator ordering for an evolution timestep, shown for an example system with 8 sites. Nearest-neighbor gates (salmon) couple adjacent sites, requiring an SVD-based truncation step after their application to control the bond dimension. Purple boxes represent single-site gates that act locally and do not modify the cutoff at each tensor site.
• Figure 2: Tensor network simulations of the inhomogeneous two-flavor two-beam fast flavor instability. Opposing neutrino beams each have 10 computational particles initially in each electron (right-moving) and muon (left-moving) flavor states. Mean-field results (solid curve) result from truncating the SVD using a cutoff of $c=1$ and exhibit a FFI growth rate that matches the analytic solution within $0.2\%$. The dashed curve is from an exact (i.e., $c=0$) calculation. Many-body entanglement effects occur before development of the FFI.
• Figure 3: Time evolution of the average magnitude of the $z$-component of the polarization vector $\langle|P_z|\rangle$ (top panel) and the Von-Neumann entanglement entropy $S$ averaged over all sites (bottom panel), computed without truncating the bond dimension for varying system sizes $N_\mathrm{sites}$. Increasing $N_\mathrm{sites}$ delays the onset of significant flavor transformation, shifting both the time of the first minimum ($t_\mathrm{min}$) and the peak entropy to later times.
• Figure 4: Time evolution of the polarization component $\langle|P_z|\rangle$ (top panel) and Von-Neumann entanglement entropy (bottom panel) for $N_\mathrm{sites}=24$, comparing fully-entangled (exact) simulations (black dashed line) with truncated simulations at varying singular-value decomposition thresholds $c$. Larger cutoff values (blue) result in mean-field behavior. Due to the large errors in the $c=10^{-2}$ and $10^{-3}$ calculations, we restrict our later analysis to $c=10^{-4}$, $10^{-5}$, and 0 as given in Table \ref{['tab:fit_parameters']} and Fig. \ref{['fig:extrapolate']}
• Figure 5: Scaling behavior of the first minimum time $t_\mathrm{min}$ of the polarization component $\langle |P_z|\rangle$ with system size $N_\mathrm{sites}$, computed for different cutoff values: $c=0$ (black dots), $c=10^{-5}$ (red stars), and $c=10^{-4}$ (gray crosses). The curves represent fits to the $c=0$ data using a logarithmic (solid curve) and square root (dotted curve) function. The logarithmic function consistently provides a superior fit for the exact data, with RMS errors significantly lower (see Table \ref{['tab:fit_parameters']}).