High-order harmonic generation and dynamic localization in a driven two-level system, a non-perturbative solution using the Floquet–Green formalism

Emergent symmetries in prethermal phases of periodically driven quantum systems

Periodically driven closed quantum systems are expected to eventually heat up to infinite temperature; reaching a steady state described by a circular orthogonal ensemble. However, such finite driven systems may exhibit sufficiently long prethermal regimes; their properties in these regimes are qualitatively different from that of their corresponding infinite temperature steady states. These, often experimentally relevant, prethermal regimes host a wide range of phenomena; they may exhibit dynamical localization and freezing, host Floquet scars, display signatures of Hilbert space fragmentation, and exhibit time crystalline phases. Such phenomena are often accompanied by emergent approximate dynamical symmetries which have no analogue in equilibrium systems. In this review, we provide a pedagogical introduction to the origin and nature of these symmetries and discuss their role in shaping the prethermal phases of a class of periodically driven closed quantum systems.