Geometry and black holes in periodically driven critical quantum systems

While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. In this talk I will discuss such an exceptional class in periodically driven critical (1+1)-dimensional systems with a spatially modulated time-evolution operator described by a conformal field theory (CFT). I will show that such Floquet drives display both heating and non-heating phases, and that the heating phase can be interpreted as dynamical propagation of excitations through a curved space-time obtained by two black hole horizons, resulting in a singular concentration of energy at their center. Finally, I will present a new geometric approach to study generic inhomogeneous Floquet drives, generalising previous results that used only the finite-dimensional sl(2) algebra to systems that require the full use of the infinite-dimensional Virasoro algebra, exhibiting a richer phase diagram structure.