We consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows access to the exact time evolution in this driven quantum system. We compute time-evolved one- and two-point functions following a quench that activates the driving. It is shown that this model does not heat up to infinite temperature, despite the absence of energy conservation, and we further discuss the generalization to a family of driven Hamiltonians that do not appear to suffer heating to infinite temperature, despite the absence of integrability and disorder. The particular model studied in detail also presents a route for realizing exotic physics (in this case, signatures of the $E_8$ structure associated with perturbing a critical quantum Ising chain with a small longitudinal magnetic field) by suitably tuning the driving frequency. In particular, we numerically confirm that the ratio of the masses of the two lowest meson excitations is given by the golden ratio.

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• Quantum quench
• Ising model
• Spin chains