Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

二维 (2D) 平衡晶体的熔化是一种复杂的现象，其特征是位置和取向顺序的连续丢失。与被动系统相比，主动晶体可以通过其固有的运动性和固有的非平衡应力自组装并熔化成活性流体。目前，对活性结晶和熔化过程的非平衡物理还不是很了解。在这里，我们使用广义的 Toner-Tu 理论建立并研究了 2D 活性流体中自组织涡旋晶体的熔化。通过执行广泛的流体动力学模拟，我们发现了丰富的过渡场景。在小域上，我们确定了一个滞后过渡以及一个以活动涡格和活动湍流的时间共存为特征的过渡，两者都可以通过自我推进和主动应力来控制。在大域上，在对应于活动涡旋晶格的参数范围内形成具有固体有序的活动涡旋晶体。该晶体的熔化通过中间六相进行。通常，这些结果突出了活性流体中结晶相与其平衡对应物之间的差异和相似之处。