Floquet insulators and lattice fermions beyond naive time discretization
- URL: http://arxiv.org/abs/2311.05686v1
- Date: Thu, 9 Nov 2023 19:00:04 GMT
- Title: Floquet insulators and lattice fermions beyond naive time discretization
- Authors: Thomas Iadecola, Srimoyee Sen, Lars Sivertsen
- Abstract summary: Floquet insulators can host topologically protected bound states that exhibit response at half the frequency of the drive.
Such states can also appear in undriven lattice field theories when time is discretized as a result of fermion doubling.
We show that spectral features characteristic of beyond-equilibrium physics in Floquet systems can be replicated in static systems with appropriate time discretization.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Periodically driven quantum systems known as Floquet insulators can host
topologically protected bound states known as "$\pi$ modes" that exhibit
response at half the frequency of the drive. Such states can also appear in
undriven lattice field theories when time is discretized as a result of fermion
doubling, raising the question of whether these two phenomena could be
connected. Recently, we demonstrated such a connection at the level of an
explicit mapping between the spectra of a continuous-time Floquet model and a
discrete-time undriven lattice fermion model. However, this mapping relied on a
symmetry of the single-particle spectrum that is not present for generic drive
parameters. Inspired by the example of the temporal Wilson term in lattice
field theory, in this paper we extend this mapping to the full drive parameter
space by allowing the parameters of the discrete-time model to be
frequency-dependent. The spectra of the resulting lattice fermion models
exactly match the quasienergy spectrum of the Floquet model in the
thermodynamic limit. Our results demonstrate that spectral features
characteristic of beyond-equilibrium physics in Floquet systems can be
replicated in static systems with appropriate time discretization.
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