Novel phases in an accelerated exclusion process

We introduce a class of distance-dependent interactions in an accelerated exclusion process (AEP) inspired by the cooperative speed-up observed in transcribing RNA polymerases. In the simplest scenario, each particle hops to the neighboring site if vacant \emph{and} when joining a cluster of particles, triggers the frontmost particle to hop. Through both simulation and theoretical work, we discover that the steady state of AEP displays a discontinuous transition with periodic boundary condition. The system transitions from being homogeneous (with augmented currents) to phase-segregated. More surprisingly, the current-density relation in the phase-segregated state is simply $J=1-\rho$, indicating the particles (or holes) are moving at unit velocity despite the inclusion of long-range interactions.