Active matter systems often exhibit dynamic and static properties that are highly distinct from thermal equilibrium, including motility-induced phase separation, active turbulence, and crystallization in low dimensions. Bacterial suspension is one typical example, in which self-propelled bacteria move and interact with others, leading to complex, emergent behaviors. Recently, H. Lama et al. (2024) experimentally showed that two-dimensional dense suspension of E. Coli has two glassy transitions at different densities, where the orientational and translational degrees of freedom become dynamically arrested, respectively. They further found that the exponent for the critical divergence of the relaxation time is smaller than the lower-bound of the mode-coupling theory for equilibrium glassy systems. While this suggests the glassy transition to be qualitatively different from the equilibrium counterpart, the origin of the small exponent remains unclear.

Here, we propose a minimal active model for dense bacterial suspension in two dimensions and numerically study its dynamics and statics. In our model, each bacterium is represented by a spherocylinder of fixed length, with its state specified by position of the center of mass and orientation. Bacteria interact with each other via a short-range repulsive interaction and actively move in the direction of its orientation. To mimic the tumbling motion of bacteria in a crowded environment, we further incorporate in the model stochastic velocity reversal with a fixed rate per unit time.

With increasing density, the orientational dynamics of the system drastically slows down and its relaxation time shows a rapid growth, suggesting the critical divergence at a finite density \phi_c. On the other hand, even at \phi_c, the translational dynamics has a short relaxation time and bacteria can easily change their positions, with their orientations virtually fixed for a very long time. These dynamical properties are consistent with the experiment. Despite the long time scale for the bacterial orientation, the nematic order remains short ranged, again consistent with the experimental results. However, we find that the length scale of the ‘tetratic’ fourfold orientational order grows much faster than that of the nematic order when approaching \phi_c, indicating that the slow orientational dynamics is controlled by this orientational order. We will also discuss the collective orientational and translational dynamics near \phi_c.