A quantum critical system described at low energy by a conformal field theory(CFT) and subjected to a time-periodic boundary drive displays multipledynamical regimes depending on the drive frequency. We compute the behavior ofquantities including the entanglement entropy and Loschmidt echo, confirminganalytic predictions from field theory by exact numerics on the transversefield Ising model, and demonstrate universality by adding non-integrableperturbations. The dynamics naturally separate into three regimes: aslow-driving limit, which has an interpretation as multiple quantum quencheswith amplitude corrections from CFT; a fast-driving limit, in which the systembehaves as though subject to a single quantum quench; and a crossover regimedisplaying heating. The universal Floquet dynamics in all regimes can beunderstood using a combination of boundary CFT and Kibble-Zurek scalingarguments.
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