Closed- and open-system characterization of the Yukawa-SYK model in real time

Strongly correlated matter without quasiparticles is central to many-body physics, quantum chaos, and quantum gravity, motivating a considerable effort toward its realization in tabletop experiments. Two challenges remain: laboratory platforms are open systems, so conformal behavior must survive dissipation, and it must be identified through measurable quantities. We address both challenges in the Yukawa-Sachdev-Ye-Kitaev (YSYK) model, in which bosons and fermions interact as in, e.g., light-matter systems, but through random all-to-all couplings that drive the boson to criticality without fine tuning. Solving the model in real time using the Schwinger-Keldysh formalism, we treat closed and open systems within a unified framework and, in both cases, consider a thermal steady state to map their phase diagrams. In addition to the known conformal and impurity (or SYK$_2$) regimes, we identify novel high-temperature regimes in which the fermions are driven by an essentially bare boson and show that their dynamics is captured by a quadratic model with time-dependent random hopping. Across all regimes, the fermionic softening of the boson is bounded by a ``criticality budget'' determined only by the Yukawa coupling and the temperature. Coupling the boson with a thermal environment induces a mass shift that deforms the boundaries between different regimes and exhausts the criticality budget, thus imposing a bound on temperature and dissipation rate compatible with self-tuned criticality. We further introduce a set of markers built from the two-point functions that separate all identified regimes, are accessible in linear response, and require no fit of the conformal exponents. We complement them with the quantum Fisher information, deriving upper bounds with and without dissipation. These results may help characterize holographic quantum matter beyond the closed setting.