Dynamics of topological defects in the presence of non-reciprocal interactions: twisting, stabilisation and enhanced annihilation

We introduce an extension of the celebrated 2D XY model with non-reciprocal couplings, where short-range spin-spin interactions are weighted by a smooth anisotropic kernel. We investigate the dynamics of localised, non-reciprocal topological defects (vortices), responsible for the emergence of a Kosterlitz-Thouless transition in the reciprocal, equilibrium, case. We show that in addition to the topological charge, the actual shape of the defects, that can be characterized with a scalar, is crucial to faithfully describe their dynamics. Non-reciprocal interactions render some defect shapes unstable, twisting the field around them and radically affecting defect-defect interactions. Non-reciprocity leads to effective transverse forces, which at the defect/defect level, result in a variety of scenarios, such as very fast attraction and annihiliation, long-term stabilisation and spontaneous defect generation, strongly impacting the large-scale behaviour of the system.