Floquet Dynamics of Boundary-Driven Systems at Criticality

Area of Science:

• Condensed matter physics
• Quantum dynamics
• Statistical mechanics

Background:

• Quantum critical systems near absolute zero exhibit unique properties.
• Conformal field theory (CFT) describes low-energy physics of many quantum critical systems.
• Time-periodic driving (Floquet engineering) allows control over quantum states.

Purpose of the Study:

• To investigate the dynamical regimes of a quantum critical system under time-periodic boundary driving.
• To confirm analytic predictions from conformal field theory (CFT) using numerical methods.
• To demonstrate the universality of these dynamics, even with perturbations.

Main Methods:

• Analytical calculations using boundary conformal field theory (CFT).
• Exact numerical simulations on the transverse field Ising model.
• Introduction of nonintegrable perturbations to test universality.

Main Results:

• Identified three distinct dynamical regimes: slow-driving, fast-driving, and a crossover regime with heating.
• Confirmed that slow driving corresponds to multiple quantum quenches with CFT amplitude corrections.
• Showed fast driving mimics a single quantum quench.
• Verified universal Floquet dynamics across all regimes.

Conclusions:

• The dynamics of periodically driven quantum critical systems are universal and can be categorized into distinct regimes.
• Boundary CFT and Kibble-Zurek scaling provide a unified framework for understanding these universal dynamics.
• This work bridges analytical theory and numerical simulations for driven quantum systems.