Phase transitions in non-reciprocal active systems

Abstract

Crowds, flocks of sheep, robotic swarms or firing neurons are examples of active systems composed of energy harvesting units that move or interact according to the state of their neighbours. The interaction between two such agents is not necessarily subject to physical constraints such as Newton's third law - it can be visibly non-reciprocal, as we demonstrate using programmable robots. While non-reciprocal active media are known to exhibit non-Hermitian responses and wave phenomena, the nature of the phase transitions between their many-body phases remains elusive. Here, we show that microscopic non-reciprocity can persist at large scales and give rise to unique many-body phases and transitions controlled by singularities called exceptional points. We illustrate this mechanism within a framework that encompasses non-reciprocal generalizations of the Vicsek model of flocking and the Kuramoto model of synchronization. Our simulations and continuum theories reveal generic features of non-reciprocal matter ranging from exceptional-point enforced pattern formation to active time-(quasi)crystals. Besides active materials and collective robotics, our work sheds light on phase transitions in other non-reciprocal systems ranging from networks of neurons to ecological predator-prey models.