Defects Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors

We consider a non-equilibrium extension of the two-dimensional (2D) XY model, equivalent to the noisy Kuramoto model of synchronization with short-range coupling, where rotors sitting on a square lattice are self-driven by random intrinsic frequencies. We study the static and dynamic properties of topological defects (vortices) and establish how self-spinning affects the Berezenskii-Kosterlitz-Thouless phase transition scenario. The non-equilibrium drive breaks the quasi-long-range ordered phase of the 2D XY model into a mosaic of ordered domains of controllable size and results in self-propelled vortices that generically unbind at any temperature, featuring superdiffusion $\langle r^2(t)\rangle\sim t^{3/2}$ with a Gaussian distribution of displacements. Our work provides a simple framework to investigate topological defects in active matter and sheds new light on the problem of synchronization of locally coupled oscillators.