Anti-hyperuniform Critical States of Active Topological Defects

Abstract: Topological defects are fundamental to the collective dynamics of non-equilibrium systems and in active matter, mediating spontaneous flows, dynamic self-organization, and emergent pattern formation. Here, we reveal critical states in active nematics, marked by slowed defect density relaxation, amplified fluctuations, and heightened sensitivity to activity. Near criticality, defect interactions become long-ranged, scaling with system size, and the system enters an anti-hyperuniform regime with giant number fluctuations of topological defects and defect clustering. This transition reflects a dual scaling behavior: fluctuations are uniform at small scales but become anti-hyperuniform at larger scales, \tm{as supported by experimental measurements on large-field-of-view endothelial monolayers. We find that these anti-hyperuniform states with multiscale defect density fluctuations are robust to varying parameters, introducing frictional damping, and changing boundary conditions.} Finally, we show that the observed anti-hyperuniformity originates from defect clustering, distinguishing this transition from defect-unbinding or phase separation processes. Beyond fundamental implications for non-equilibrium systems, these results may inform biological contexts where topological defects are integral to processes such as morphogenesis and collective cellular self-organization.