  In this work, we study non-equilibrium dynamics in Floquet conformal field
theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the
energy-momentum density spatially modulated by an arbitrary smooth function.
This generalizes earlier work which was restricted to the sine-square deformed
type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra.
Here we show remarkably that the problem remains soluble in this generalized
case which involves the full Virasoro algebra, based on a geometrical approach.
It is found that the phase diagram is determined by the stroboscopic
trajectories of operator evolution. The presence/absence of spatial fixed
points in the operator evolution indicates that the driven CFT is in a
heating/non-heating phase, in which the entanglement entropy grows/oscillates
in time. Additionally, the heating regime is further subdivided into a
multitude of phases, with different entanglement patterns and spatial
distribution of energy-momentum density, which are characterized by the number
of spatial fixed points. Phase transitions between these different heating
phases can be achieved simply by changing the duration of application of the
driving Hamiltonian. We demonstrate the general features with concrete CFT
examples and compare the results to lattice calculations and find remarkable
agreement.
