Non-Reciprocal Landau-Ginzburg Theories

The study of critical phases for systems out of equilibrium has a wide range of applicability including soft matter physics, open quantum system and biological systems. In critical phenomena at equilibrium, the study of the emergent conformal symmetry at a phase transition provides a way to systematically classify critical behavior. Unlike their equilibrium counterparts, non-equilibrium criticality does not in general lead to the standard conformal group as an emergent symmetry group. In particular, time and space do not scale in the same way which leads to a dynamical critical exponent, z, which differs from 1. This difference makes a systematic understanding of non-equilibrium criticality challenging. We show that non-reciprocal interactions can lead to an emergent sound mode that dominates the low energy behavior of the physical system. This emergent sound mode gives us a dynamical critical exponent z=1 and simplifies the study of critical phases. We use this to build non-reciprocal Landau-Ginzburg theories and discuss their physical properties.