  The quantum kicked rotor is well-known for displaying dynamical (Anderson)
localization. It has recently been shown that a periodically kicked Tonks gas
will always localize and converge to a finite energy steady-state. This
steady-state has been described as being effectively thermal with an effective
temperature that depends on the parameters of the kick. Here we study a
generalization to a quasi-periodic driving with three frequencies which,
without interactions, has a metal-insulator Anderson transition. We show that a
quasi-periodically kicked Tonks gas goes through a dynamical many-body
delocalization transition when the kick strength is increased. The localized
phase is still described by a low effective temperature, while the delocalized
phase corresponds to an infinite-temperature phase, with the temperature
increasing linearly in time. At the critical point, the momentum distribution
of the Tonks gas displays different scaling at small and large momenta
(contrary to the non-interacting case), signaling a breakdown of the
one-parameter scaling theory of localization.
