Strong coupling between matter and quantized electromagnetic modes may offer yet another approach of controlling equilibrium phases or dynamics of quantum many-body systems. Recent developments have realized such strong light-matter interaction in genuinely nonperturbative regimes, where conventional theoretical methods often fail. I will talk about how one can analyze strongly coupled quantum light-matter systems at arbitrary interaction strengths on the basis of an asymptotically disentangling unitary transformation [1,2]. I discuss its application to construction of tight-binding Hamiltonians, dynamics of bound states in the continuum, and revisiting dissipative quantum phase transition in resistively shunted Josephson junctions .
 Y. Ashida, A. Imamoglu and E. Demler, PRL 126, 153603 (2021).
 Y. Ashida, T. Yokota, A. Imamoglu and E. Demler, PRR 4, 023194 (2022).
 K. Masuki, H. Sudo, M. Oshikawa and Y. Ashida, PRL 129, 087001 (2022).