Geometric approach to inhomogeneous Floquet systems

We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical the circle that we establish and use prove existence of (non)heating phases characterized (absence) presence fixed or higher-periodic points coordinate transformations encoding time evolution: Heating corresponds energy excitations concentrating exponentially fast at unstable such while nonheating pseudoperiodic motion. show heating rate (serving as order parameter for transitions between these two) can have cusps, even within overall phase, there rich structure phase diagrams different distinguishable through kinks entanglement entropy, reminiscent Lifshitz transitions. Our generalizes previous results subfamily similar used only $\mathfrak{sl}(2)$ algebra general smooth deformations require full infinite-dimensional Virasoro algebra, argue it has wider applicability, beyond theory.