Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws

Abstract

Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities (LCQ) is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant "conservation laws" in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics has a much richer structure due to the existence of {\it emergent} conservation laws: these are approximate but stable conservation laws arising {\it due to the drive}, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp ergodicity threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This opens up a new possibility of stable Floquet engineering in such systems. This review intends to give a theoretical overview of these developments. We conclude by briefly surveying the experimental scenario.

Invited Review for Journal of Physics: Condensed Mattter

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Cited by in corpus (22)

• Non-Hermitian Floquet Topological Matter -- A Review
• Bounds in Nonequilibrium Quantum Dynamics
• Discrete time crystal enabled by Stark many-body localization
• Fermi's golden rule for heating in strongly driven Floquet systems
• Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Dynamical localization and slow dynamics in quasiperiodically-driven quantum systems
• Analytical theory of cat scars with discrete time crystalline dynamics in Floquet systems
• Interferometry based on quantum Kibble-Zurek mechanism
• Entanglement dynamics and phase transitions of the Floquet cluster spin chain
• Exact many-body scars based on pairs or multimers in a chain of spinless fermions
• Floquet States
• Counterdiabatic Route to Entanglement Steering and Dynamical Freezing in the Floquet Lipkin-Meshkov-Glick Model
• Prethermalization in aperiodically driven classical spin systems
• Arresting Quantum Chaos Dynamically in Transmon Arrays
• Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
• Dynamical freezing and switching in periodically driven bilayer graphene
• Stretched-Exponential Melting of a Dynamically Frozen State Under Imprinted Phase Noise in the Ising Chain in a Transverse Field
• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems
• Time crystal embodies chimeralike state in periodically driven quantum spin system
• Long-time properties of generic Floquet systems are approximately periodic with the driving period
• Floquet-Engineered Valley-Topotronics in Kekulé-Y Bond Textured Graphene Superlattice