A Complex Topological Phase in C-Spin Active Matter

This work unveils complex topological properties within a recent theoretical model concerning the interplay of positional and orientational order. The model features "complementary-spins" (c-spins), symbolic agents divided into two populations with contrasting positional and orien-tational interactions. The model is governed by a control parameter, a form of circular anisot-ropy that splits the c-spins natural rotational frequencies. For a given system size and for small anisotropy, uniform equilibrium patterns showing both positional and orientational regularity emerge, consistently with local stability predictions. For moderate anisotropy, the system de-velops complex topological point defects, driven by phase singularity and bistable with the uniform patterns. The defects are constituted by curled orientational textures embedding two c-spin loop trains that counter-rotate around the same center, exhibiting regular spacing, spin-momentum locking and dissipationless flow. These defect complexes are extremely robust to noise and capable of self-repair, and constitute a whole new class of non-equilibrium dissi-pative structures. These are in fact topological vortex states, classifiable by a two-valued topo-logical charge. For anisotropy values exceeding a local stability threshold, active turbulence (deterministic chaos) takes place and order is lost. A statistical analysis revealed the coexistence of a double phase transition at a critical parameter value: an "ordinary" symmetry-breaking transition associated with standard collective synchronization and a novel topological phase transition activating the vortex complexes. Quantitative boundaries in the parameter space have been evaluated, either analytically or numerically. Increasing system size enhances organiza-tional complexity, developing more intricate spin-momentum locked transport networks. Thanks to its self-organizational properties, this work provides a new tool to understand ro-bustness and morphogenesis in living systems.