Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class

The height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) growth in 1+1 dimensions are sensitive to the initial state. Here we focus on height fluctuations in the stationary regime described by the Baik-Rains distribution. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. Going into more detail, the conditioned probability distribution of an initial state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative height fluctuations that are dominated by super-diffusive shock dynamics. Two possible point-symmetric shock profiles cause the bimodality and the KPZ mirror symmetry breakdown. To establish universality of our findings we demonstrate scale invariance at different times and heights using large-scale Monte-Carlo simulations of the totally asymmetric simple exclusion process (TASEP) which belongs to the KPZ universality class.