Topological Origin of Floquet Thermalization in Periodically Driven Many-body Systems

Floquet engineering is a powerful manipulation method in modern quantum technology. However, unwanted heating is the main challenge of Floquet engineering, therefore the Floquet thermalization has attracting considerable attentions recently. In this work, we investigate thermalization of periodically driven many-body systems through the lens of Krylov complexity, and find a topological origin of different thermalization behaviors. We demonstrate that If the topology of the Krylov chain is nontrivial, a periodically driven system will reach a state with finite temperature. When the Krylov chain is topologically trivial, the system will be heated to infinite temperature. We further show that the prethermalization can be understood as the tunnelling process of a quasi-edge mode through the local gap on Krylov chain. This picture provides a systematically method to obtain the effective prethermal Hamiltonian.