Floquet Dynamics of Boundary-Driven Conformal Field Theories

We study the dynamics of quantum critical 1D systems described by a conformal field theory (CFT) subject to a periodic boundary drive. We focus on the transverse-field Ising CFT with a boundary field step-drive, and analytically and numerically calculate its entanglement entropy and Loschmidt echo. We identify three regimes with distinct dynamics, and show that two are well-described by boundary CFT: a slow-driving limit where the Loschmidt echo is given by an N-point function of boundary condition changing operators, and a fast-driving limit where the Floquet-Magnus high-frequency Hamiltonian converges to a single quench at half field, plus irrelevant terms. An intermediate regime governed by resonant processes produces extensive entropy and dynamics described by quantum field theory. We comment on generalizations to other kinds of boundary drives and CFTs, and on applications to quenches involving $\pi$-Majorana fermions.