A geometric approach to inhomogeneous Floquet systems

We present a new geometric approach to study Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. By encoding the time evolution into coordinate transformations, we show existence of heating phases characterized by fixed or higher-periodic points of these transformations, with energy and excitations concentrating exponentially at unstable such points. The heating rate serves as order parameter for transitions between heating and non-heating and can change both smoothly and non-analytically, even within the overall heating phase. Our results lead to a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. The proposed geometric approach generalizes previous results for a small subfamily of similar systems that used only the $\mathfrak{sl}(2)$ algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it and the underlying ideas have a wider applicability, even beyond CFT.