Emergent black hole dynamics in critical Floquet systems

Abstract

While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. We study such an exceptional class in periodically driven critical (1+1)-dimensional systems with a spatially modulated but disorder-free time evolution operator. Instead of complete scrambling, the excitations of the system remain well defined. Their propagation is analogous to the evolution along light cones in a curved spacetime obtained by two black holes. The Hawking temperature serves as an order parameter which distinguishes between heating and nonheating phases. Beyond a timescale determined by the inverse Hawking temperature, excitations are absorbed by the black holes resulting in a singular concentration of energy at their horizon. We obtain these results analytically within conformal field theory, capitalizing on a mapping to sine-squared deformed field theories. Furthermore, by means of numerical calculations for an interacting XXZ spin-12 chain, we demonstrate that our findings survive lattice regularization.