Emergent symmetries in prethermal phases of periodically driven quantum systems

TL;DR

This paper reviews how emergent approximate symmetries in periodically driven quantum systems lead to rich prethermal phases, distinct from their eventual thermalized states, with implications for dynamical localization, scars, and time crystals.

Contribution

It provides a pedagogical overview of the origin and role of emergent symmetries in prethermal phases of driven quantum systems, highlighting their novel features.

Findings

Emergent symmetries underpin prethermal phenomena.

Prethermal regimes exhibit localization, scars, and time crystals.

Symmetries differ from equilibrium counterparts.

Abstract

Periodically driven closed quantum systems are expected to eventually heat up to infinite temperature reaching a steady state described by a circular orthogonal ensemble (COE). However, such finite driven systems may exhibit sufficiently long prethermal regimes; their properties in these regimes are qualitatively different from that in their 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.