Long-range Order and Directional Defect Propagation in the Nonreciprocal XY Model with Vision Cone Interactions

We study a two-dimensional, nonreciprocal XY model, where each spin interacts only with its nearest neighbours in a certain angle around its current orientation, i.e., its `vision cone'. Using energetic arguments and Monte-Carlo simulations we show that a true long-range ordered phase emerges. A necessary ingredient is a configuration-dependent bond dilution entailed by the vision cones. Strikingly, defects propagate in a directional manner, thereby breaking the parity and time-reversal symmetry of the spin dynamics. This is detectable by a non-zero entropy production rate.