Symmetry-restoring crossover from defect-free to defect-laden turbulence in polar active matter

Coherent flows of self-propelled particles are characterized by vortices and jets that sustain chaotic flows, referred to as active turbulence. Here, we reveal a crossover between defect-free active turbulence and active turbulence laden with topological defects. Interestingly, we show that concurrent to the crossover from defect-free to defect-laden active turbulence is the restoration of the previously broken $\SO(2)$-symmetry signaled by the fast decay of the two-point correlations. By stability analyses of the topological charge density field, we provide theoretical insights on the criterion for the crossover to the defect-laden active turbulent state. Despite the distinct symmetry features between these two active turbulence regimes, the flow fluctuations exhibit universal statistical scaling behaviors at large scales, while the spectrum of polarity fluctuations decays exponentially at small length scales compared to the active energy injection length. These findings reveal a new dynamical crossover between distinct spatiotemporal organization patterns in polar active mater.