On the Entanglement and Energy Dynamics of Continuous Floquet-driven CFTs

A key approach to studying non-equilibrium quantum many-body systems is to suddenly alter their Hamiltonian and observe the resulting dynamical evolution. A single change is called a "quench", while periodic changes are termed "Floquet driving". Recently, Floquet driving protocols in two-dimensional conformal field theories (CFTs) have attracted widespread attention due to their exact solvability and rich phase structure. However, most studies are limited to discrete-type driving (e.g., as a square wave) and the associated stroboscopic dynamics (i.e., evolution at integer multiples of the driving period). A key obstacle is that a generic continuous driving is rarely analytically tractable. In this talk, I will introduce a class of exactly solvable continuous Floquet driving protocols. I will discuss the energy and entanglement dynamics under these protocols in 2D CFTs, as well as their holographic duals. Crucially, the results show that stroboscopic dynamics, if overinterpreted, can qualitatively misrepresent the system’s true continuous-time evolution.