Floquet Insulators and Lattice Fermions

Area of Science:

• Quantum physics
• Condensed matter physics
• Topological phases

Background:

• Floquet insulators are quantum systems subjected to periodic driving, leading to unique topological phases.
• These phases share characteristics with fermion doubling phenomena observed in discrete-time lattice fermion theories.

Purpose of the Study:

• To concretely demonstrate the connection between Floquet insulator phases and discrete-time lattice fermion theories.
• To map the spectral properties of a specific Floquet insulator model to a time-independent Hamiltonian.

Main Methods:

• Analysis of the spectrum of a noninteracting (1+1)D Floquet insulator under specific drive parameters.
• Mapping this spectrum onto a discrete-time lattice fermion theory with a time-independent Hamiltonian.

Main Results:

• The mapping results in a Hamiltonian distinct from the stroboscopic Floquet Hamiltonian.
• The derived Hamiltonian can represent a discrete-time Su-Schrieffer-Heeger model with half the original spatial sites.
• Alternatively, it can manifest as a (1+1)D Wilson-Dirac theory with one quarter of the original spatial sites.

Conclusions:

• Periodically driven Floquet insulators can effectively realize discrete-time lattice fermion models.
• This provides a new perspective on topological phases in driven quantum systems and their relation to lattice field theories.