The necessity of using more rigorous models is substantiated by the recent progress of experimentation in recent years. For example, the Ebbesen group in Ref. 40 achieved ultra-strong light-matter coupling in a Fabry-Pérot cavity with an effective g c √ N /ω c = 0.16. Additionally, for single molecules in plasmonic cavities, the Baumberg group in Ref. 20 demonstrates strong coupling that was nearly in the ultrastrong regime. These seminal experiments cannot be accurately described with the simple JC and TC models. In this man-ner, there has been a significant push in recent years to advance the theoretical understanding and simulations for these systems to explain current experiments and predict future ones.