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.
 J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, Phys. Rev. Lett. 101, 255702 (2008).
 G. Lemarié, H. Lignier, D. Delande, P. Szriftgiser, and J. C. Garreau, Phys. Rev. Lett. 105, 090601 (2010).
 M. Lopez, J.-F. Clément, P. Szriftgiser, J. C. Garreau, and D. Delande, Phys. Rev. Lett. 108, 095701 (2012).
 I. Manai, J.-F. Clément, R. Chicireanu, C. Hainaut, J. C. Garreau, P. Szriftgiser, and D. Delande, Phys. Rev. Lett. 115, 240603 (2015).
 M. Serbyn, Z. Papić, and D. A. Abanin, Phys. Rev. Lett. 111, 127201 (2013).
 P. Ponte, Z. Papić, F. m. c. Huveneers, and D. A. Abanin, Phys. Rev. Lett. 114, 140401 (2015a).
 C. Rylands, E. B. Rozenbaum, V. Galitski, and R. Konik, Phys. Rev. Lett. 124, 155302 (2020).
 A. S. Pikovsky and D. L. Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008).
 S. Flach, D. O. Krimer, and C. Skokos, Phys. Rev. Lett. 102, 024101 (2009).
 N. Cherroret, B. Vermersch, J. C. Garreau, and D. Delande, Phys. Rev. Lett. 112, 170603 (2014).
 A. Cao, R. Sajjad, H. Mas, E. Q. Simmons, J. L. Tanlimco, E. Nolasco-Martinez, T. Shimasaki, H. E. Kondakci, V. Galitski, and D. M. Weld, Nature Physics 18, 1302 (2022).
 L. Ermann and D. L. Shepelyansky, Journal of Physics A: Mathematical and Theoretical 47, 335101 (2014).
 M. Lopez, J.-F. Clément, G. Lemarié, D. Delande, P. Szriftgiser, and J. C. Garreau, New Journal of Physics 15, 065013 (2013).
 H. Buljan, R. Pezer, and T. Gasenzer, Phys. Rev. Lett. 100, 080406 (2008).
 P. Vignolo and A. Minguzzi, Phys. Rev. Lett. 110, 020403 (2013).
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