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Entanglement asymmetry in periodically driven quantum systems
Tista Banerjee (Indian Association for the Cultivation of Science), Suchetan Das (Indian Association for the Cultivation of Science), K. Sengupta (Indian Association for the Cultivation of Science)
Résumé : We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, \Delta S Δ S , as a function of the drive frequency. Our analysis identifies special drive frequencies at which the driven XY chain exhibits dynamic symmetry restoration and displays quantum Mpemba effect over a long timescale; we identify an emergent approximate symmetry in its Floquet Hamiltonian which plays a crucial role for realization of both these phenomena. We follow these results by numerical computation of \Delta S Δ S for the non-integrable driven Rydberg atom chain and obtain similar emergent-symmetry-induced symmetry restoration and quantum Mpemba effect in the prethermal regime for such a system. Finally, we provide an exact analytic computation of the entanglement asymmetry for a periodically driven conformal field theory (CFT) on a strip. Such a driven CFT, depending on the drive amplitude and frequency, exhibits two distinct phases, heating and non-heating, that are separated by a critical line. Our results show that for m m cycles of a periodic drive with time period T T , \Delta S \sim \ln mT Δ S ∼ ln m T [ \ln (\ln mT) ln ( ln m T ) ] in the heating phase [on the critical line] for a generic CFT; in contrast, in the non-heating phase, \Delta S Δ S displays small amplitude oscillations around it’s initial value as a function of mT m T . We provide a phase diagram for the behavior of \Delta S Δ S for such driven CFTs as a function of the drive frequency and amplitude.