Motility Induced Phase Separation and Frustration in Active Matter Swarmalators

We introduce a system of active matter swarmalators composed of elastically interacting run-and-tumble active disks with an internal phase $\phi_i$. The disks experience an additional attractive or repulsive force with neighboring disks depending upon their relative difference in $\phi_i$. In the absence of the internal phase, the system forms a Motility-Induced Phase Separated (MIPS) state, but when the swarmalator interactions are present, a wide variety of other active phases appear depending upon whether the interaction is attractive or repulsive and whether the particles act to synchronize or anti-synchronize their internal phase values. These include a gas-free gel regime, arrested clusters, a labyrinthine state, a regular MIPS state, a frustrated MIPS state for attractive anti-synchronization, and a superlattice MIPS state for attractive synchronization.