  Quantum light-matter systems at strong coupling are notoriously challenging
to analyze due to the need to include states with many excitations in every
coupled mode. We propose a nonperturbative approach to analyze light-matter
correlations at all interaction strengths. The key element of our approach is a
unitary transformation that achieves asymptotic decoupling of light and matter
degrees of freedom in the limit where light-matter interaction becomes the
dominant energy scale. In the transformed frame, truncation of the
matter/photon Hilbert space is increasingly well-justified at larger coupling,
enabling one to systematically derive low-energy effective models, such as
tight-binding Hamiltonians. We demonstrate the versatility of our approach by
applying it to concrete models relevant to electrons in crystal potential and
electric dipoles interacting with a cavity mode. A generalization to the case
of spatially varying electromagnetic modes is also discussed.
