When irrelevance governs: dissipation-regression scaling in open quantum criticality

The real-time dynamics of quantum phase transitions in open systems coupled to finite-temperature environments sits at the heart of contemporary condensed-matter and quantum-information science. Here, invoking a Schwinger-Keldysh formalism, we uncover that, within the coherence-dominated regime of critical real-time evolution, a dissipative coupling deemed naively irrelevant determines, counterintuitively, the longest timescale that holds sway. Possessing a well-defined temporal scaling dimension, it engenders a novel dissipation-regression scaling that systematically reproduces the unusual Kibble-Zurek scaling and relaxation observed in recent numerical studies. By contrast, dissipation-dominated dynamics behaves qualitatively differently. There, furthermore, we show that the discretized and diagonalized formulations of the same open quantum Ising chain realize distinct universality classes.