Thermodynamic Supercriticality and Complex Phase Diagram for Charged AdS Black Holes in Trace Anomaly Gravity
We extend the Lee-Yang phase transition framework to charged anti-de Sitter (AdS) black holes in four-dimensional trace anomaly gravity. By treating the horizon radius as a complex variable, we derive a fully resolved complex phase diagram that uncovers novel supercritical phenomena within this modified gravity setting. Relative to the standard Reissner-Nordstr\"om-AdS black hole, the trace anomaly shifts the location of the critical point: for a representative set of anomaly parameters, both the critical pressure and critical temperature are suppressed. The Widom line is rigorously identified as the projection of the complex Lee-Yang zeros onto the real physical phase plane, a trajectory that demarcates the small-black-hole-like and large-black-hole-like phases throughout the supercritical regime. We also independently recover this same Widom line via the thermodynamic response function method, demonstrating that the two definitions are in excellent quantitative agreement in the near-critical region and share identical universal scaling behavior. Furthermore, our analysis reveals a smooth, continuous crossover across the Widom line as probed by thermodynamic response functions--a behavior fundamentally distinct from the discontinuous first-order phase transitions that occur below the critical point. These results offer new, physically concrete insights into the thermodynamics of quantum-corrected black holes.