Concept Guide — Floquet Workflows

Periodic driving introduces additional structure beyond static lattice Hamiltonians. The Floquet module (developed with Tobias Kästli during his Master's project) provides convenience APIs for constructing and analysing driven systems.

Core functions

• Floquet.makefloquet(hops; harmonics, ω, gauge): build the truncated Floquet Hamiltonian by stacking harmonic sectors.
• Floquet.getspectrum(floquet_hops; kwargs...): obtain quasienergies and states.
• Floquet.makeobservable(op; harmonics): lift static observables to Floquet space for expectation-value calculations.

Workflow checkpoints

1. Static baseline — Assemble the non-driven Hamiltonian using Operators.
2. Drive specification — Encode vector potentials or onsite modulations with helper functions (e.g. Floquet.circular_drive).
3. Harmonic truncation — Choose harmonic count based on drive strength; verify convergence by increasing the cutoff until spectra stabilise.
4. Diagonalisation — Solve for quasienergies; classify them modulo the drive frequency.
5. Observables — Evaluate micromotion, time-averaged expectation values, or Floquet-broadened densities of states.

Numerical tips

• Use sparse representations; Floquet Hamiltonians are block-structured and can grow rapidly with harmonic count.
• Normalise phases consistently across harmonics to avoid discontinuities in observables.
• Profile memory/time with representative parameters; record findings in the Advanced Workflows section.

Further reading

• Tutorial: Floquet Dynamics for a guided example.
• Examples: Extend the graphene scripts by adding periodic drives and compare static vs. driven observables.