Emergent polar order in nonpolar mixtures with nonreciprocal interactions

Phenomenological rules that govern the collective behavior of complex physical systems are powerful tools because they can make concrete predictions about their universality class based on generic considerations, such as symmetries, conservation laws, and dimensionality. While in most cases such considerations are manifestly ingrained in the constituents, novel phenomenology can emerge when composite units associated with emergent symmetries dominate the behavior of the system. We study a generic class of active matter systems with nonreciprocal interactions and demonstrate the existence of true long-range polar order in two dimensions and above, both at the linear level and by including all relevant nonlinearities in the Renormalization Group sense. We achieve this by uncovering a mapping of our scalar active mixture theory to the Toner-Tu theory of dry polar active matter by employing a suitably defined polar order parameter. We then demonstrate that the complete effective field theory-which includes all the soft modes and the relevant nonlinear terms-belongs to the (Burgers-) Kardar-Parisi-Zhang universality class. This classification allows us to prove the stability of the emergent polar long-range order in scalar nonreciprocal mixtures in two dimensions, and hence a conclusive violation of the Mermin-Wagner theorem.