Floquet insulators and lattice fermions

TL;DR

This paper explores the connection between Floquet insulators and lattice fermion theories, mapping their spectra to reveal fermion doubling phenomena and novel topological phases in driven quantum systems.

Contribution

It provides a concrete mapping between Floquet insulator spectra and lattice fermion theories, highlighting fermion doubling and topological features in driven systems.

Findings

Spectrum of Floquet insulators mapped onto lattice fermion theories

Identification of fermion doubling phenomena in driven systems

Connection to discrete-time SSH and Wilson-Dirac models

Abstract

Floquet insulators are periodically driven quantum systems that can host novel topological phases as a function of the drive parameters. These new phases exhibit features reminiscent of fermion doubling in discrete-time lattice fermion theories. We make this suggestion concrete by mapping the spectrum of a noninteracting (1+1)D Floquet insulator for certain drive parameters onto that of a discrete-time lattice fermion theory with a time-independent Hamiltonian. The resulting Hamiltonian is distinct from the Floquet Hamiltonian that generates stroboscopic dynamics. It can take the form of a discrete-time Su-Schrieffer-Heeger model with half the number of spatial sites of the original model, or of a (1+1)D Wilson-Dirac theory with one quarter of the spatial sites.