Anomalous Dynamical Heterogeneity in Active Glasses as a Signature of Violation of Mermin-Wagner-Hohenberg Theorem

Abstract: Two-dimensional (2D) systems have attracted renewed interest within the scientific community due to their anomalous dynamical behaviors, which arise from long-wavelength density fluctuations as predicted by the Mermin-Wagner-Hohenberg (MWH) theorem. In equilibrium, it is well established that continuous spontaneous symmetry breaking (SSB) in 2D is prohibited at any finite temperature ($T > 0$), resulting in the absence of true long-range positional order and establishing $d_l = 2$ as the lower critical dimension. Recent studies have demonstrated that, in active systems, the lower critical dimension can shift from $d_l = 2$ to $3$. This study examines the impact of MWH theorem violation in active systems on dynamical heterogeneity (DH). As a minimal model, glassy systems of active particles undergoing run-and-tumble (RT) motion are considered. Glass-like dynamical behavior, including anomalously enhanced DH, is observed in various biological systems such as collective cell migration, bacterial cytoplasm, and ant colonies. Furthermore, the study investigates the influence of local positional order, or medium-range crystalline order (MRCO), on DH in the presence of activity. The results indicate that the growth of DH with increasing activity differs significantly between systems with and without MRCO. These findings may have important implications, as many biological systems exhibit local structural ordering, and DH could serve as a useful indicator for quantifying the degree of ordering.