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

The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. 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, which belongs to the KPZ universality class. Here we focus on current (or height) fluctuations in the steady-state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial-state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by superdiffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.