LMP Seminar: Emergent polar order in non-polar mixtures with non-reciprocal interactions

Phenomenological rules that govern the collective behaviour 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 behaviour of the system. I will present the study of a generic class of active matter systems with non-reciprocal interactions where we 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. I will then show that the complete effective field theory of fluctuations -- 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 non-reciprocal mixtures in two dimensions, and hence a conclusive violation of the Mermin-Wagner theorem. Finally, I will show how to extend this dry system to a wet case, where hydrodynamic interactions are taken into consideration in the presence of a momentum-conserving fluid. The mapping to a polar active fluid is again crucial to uncover a fluid mediated linear instability for traveling waves.