Emergent Black Hole Dynamics in Critical Floquet Systems

TL;DR

This paper explores how certain periodically driven quantum systems avoid complete thermalization, exhibiting black hole-like behavior with well-defined excitations and energy concentration, analyzed through conformal field theory and numerical simulations.

Contribution

It introduces a novel class of critical Floquet systems with black hole analogs, combining analytical conformal field theory methods and numerical lattice models to reveal emergent black hole dynamics.

Findings

Excitations remain well-defined and propagate along light-cone-like trajectories.

Hawking temperature acts as an order parameter distinguishing phases.

Energy concentrates at black hole centers after a certain time scale.

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 space-time obtained by two Schwarzschild black holes. The Hawking temperature serves as an order parameter which distinguishes between heating and non-heating phases. Beyond a time scale determined by the inverse Hawking temperature, excitations are absorbed by the black holes resulting in a singular concentration of energy at their center. We obtain these results analytically within conformal field theory, capitalizing on a mapping to sine-square deformed field theories. Furthermore, by means of numerical calculations for an interacting XXZ spin-1/2 chain, we demonstrate that our findings survive lattice regularization.