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.
Highlights
Floquet quantum many-body systems provide a rich arena to explore new foundational principles of statistical physics beyond equilibrium
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 find that micromotion can lead to additional interesting features both in the conformal field theory (CFT) as well as in the physical system on a lattice
Summary
Floquet quantum many-body systems provide a rich arena to explore new foundational principles of statistical physics beyond equilibrium. The richness of SSDs was only recently unveiled via studies of both integrable lattice models such as quantum spin chains [13,14,15] and CFTs in the continuum [7,8,16,17,18,19] We verify the surprising robustness of the CFT prediction in both phases compared to the numerical study of the driven X X Z spin chain, up to about 100 cycles This suggests a possible experimental realization, for example with cold atoms in an optical lattice
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