Streamlined Krylov construction and classification of ergodic Floquet systems.

Area of Science:

• Quantum physics
• Condensed matter theory
• Quantum chaos

Background:

• Periodically driven (Floquet) quantum systems exhibit complex dynamics.
• Simulating these systems is computationally challenging.
• Existing methods for analyzing Floquet systems can be slow.

Purpose of the Study:

• To generalize the Krylov construction for simulating Floquet quantum systems.
• To develop a faster and more efficient simulation method.
• To classify Floquet systems as chaotic or integrable.

Main Methods:

• Utilizing the theory of orthogonal polynomials on the unit circle.
• Generalizing the Krylov construction to Floquet systems.
• Mapping quantum dynamics to a one-dimensional tight-binding Krylov chain.

Main Results:

• The proposed method provides a faster alternative to existing approaches.
• Any quantum dynamics in Floquet systems can be mapped to a Krylov chain.
• The asymptotic behavior of Krylov chain hopping parameters (Verblunsky coefficients) can classify Floquet systems.

Conclusions:

• The generalized Krylov construction offers an efficient tool for simulating Floquet quantum systems.
• This method facilitates the distinction between chaotic and integrable Floquet systems.
• The approach is illustrated with relevant physical models like random matrix ensembles and kicked systems.