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}_2𝔰𝔩2
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. %In general, there are rich internal structures
in the heating phase characterized by different numbers of spatial fixed
points, which result in different entanglement patterns and distribution
of energy-momentum density in space. %Interestingly, after each driving
cycle, these spatial fixed points will shuffle to each other in the
array, and come back to the original locations after
pp
(p\ge 1p≥1)
driving cycles. We demonstrate the general features with concrete CFT
examples and compare the results to lattice calculations and find
remarkable agreement.
Floquet conformal field theories with generally deformed Hamiltonians
