Two-dimensional chiral Malthusian flocks map to (2+1)-dimensional KPZ growth, so any chirality destroys long-range order but leaves a weak-chirality cascade of quasi-ordered regimes.
Kardar-Parisi-Zhang scaling in time-crystalline matter
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We discuss the universal behavior linked to the Goldstone mode associated with the spontaneous breaking of time-translation symmetry in many-body systems, in which the order parameter traces out a limit cycle. We show that this universal behavior is closely tied to Kardar-Parisi-Zhang physics, which can strongly affect the scaling properties in all dimensions. Our work predicts the relevance of KPZ in numerous systems such as nonreciprocal phases in active matter, active magnets, driven-dissipative quantum systems, and synchronization of oscillators.
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Hydrodynamic Theory of Two-dimensional Chiral Malthusian Flocks
Two-dimensional chiral Malthusian flocks map to (2+1)-dimensional KPZ growth, so any chirality destroys long-range order but leaves a weak-chirality cascade of quasi-ordered regimes.