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arXiv:2504.10601 · Physical review. D/Physical review. D.

Simulating lattice fermion doubling with a Floquet drive

Raúl A. Briceño, William Gyory, Thomas Iadecola, Srimoyee Sen

Published Nov 6, 2025• 1 citation
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Abstract

We consider a recently discovered mathematical correspondence between the spectra of a naively discretized lattice fermion and that of a periodically driven (i.e., Floquet) quantum system and enhance it into an infrared equivalence between the two systems. The equivalence can be framed as a duality relation, allowing us to simulate a two-flavor discrete-time fermion theory on the lattice side, where the two flavors arise from time discretization, using a single-flavor fermion theory on the Floquet side. Our demonstration establishes an equivalence between (i) the fermion content, (ii) the correlation functions, and consequently (iii) observables of the two theories in the infrared, going substantially beyond the previously discovered spectral equivalence. We also show how interactions may be incorporated into this enhanced infrared equivalence.

DOI
10.1103/vl1z-gl5q

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We consider a recently discovered mathematical correspondence between the spectra of a naively discretized lattice fermion and that of a periodically driven (i.e., Floquet) quantum system and enhance it into an infrared equivalence between the two systems. The equivalence can be framed as a duality relation, allowing us to simulate a two-flavor discrete-time fermion theory on the lattice side, where the two flavors arise from time discretization, using a single-flavor fermion theory on the Floquet side. Our demonstration establishes an equivalence between (i) the fermion content, (ii) the correlation functions, and consequently (iii) observables of the two theories in the infrared, going substantially beyond the previously discovered spectral equivalence. We also show how interactions may be incorporated into this enhanced infrared equivalence.
Periodically driven quantum systems known as Floquet insulators can host topologically protected bound states known as “ π 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. Published by the American Physical Society 2024
Periodically driven quantum systems defined in continuous time, also known as Floquet systems, share intriguing similarities with static/undriven lattice field theories defined in discrete time. E.g. in the former, periodic driving leads to Brillouin zone in quasi-energy space which is reminiscent of frequency Brillouin zones in the latter. These similarities lead to a natural question, {\it{is there a concrete correspondence between the two systems?}} In this work I address this question and demonstrate that there indeed exists a concrete mathematical correspondence between a certain 1+11+11+1 dimensional non-interacting Floquet system and a 1+11+11+1 dimensional lattice Dirac fermion defined on naively discretized time lattice. I also comment on the possibility of extending this type of correspondence to higher dimensional theories.
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.
2+12+12+1 dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence
A connection has recently been proposed between periodically driven systems known as Floquet insulators in continuous time and static fermion theories in discrete time. This connection has been established in a (1+1) ( 1 + 1 ) -dimensional free theory, where an explicit mapping between the spectra of a Floquet insulator and a discrete-time Dirac fermion theory has been formulated. Here we investigate the potential of static discrete-time theories to capture Floquet physics in higher dimensions, where so-called anomalous Floquet topological insulators can emerge that feature chiral edge states despite having bulk bands with zero Chern number. Starting from a particular model of an anomalous Floquet system, we provide an example of a static discrete-time theory whose bulk spectrum is an exact analytic match for the Floquet spectrum. The spectra with open boundary conditions in a particular strip geometry also match up to finite-size corrections. However, the models differ in several important respects. The discrete-time theory is spatially anisotropic, so that the spectra do not agree for all lattice terminations, e.g. other strip geometries or on half spaces. This difference can be attributed to the fact that the static discrete-time model is quasi-one-dimensional in nature and therefore has a different bulk-boundary correspondence than the Floquet model.
We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is analyzed by comparing it to an equivalent implementation in undriven systems. The dynamics of double occupancies for the near- and off-resonant driving regime indicate that the effective Hamiltonian picture is valid for several orders of magnitude in modulation time. Furthermore, we show that driving a hexagonal lattice compared to a simple cubic lattice allows us to modulate the system up to 1 s, corresponding to hundreds of tunneling times, with only minor atom loss. Here, driving at a frequency close to the interaction energy does not introduce resonant features to the atom loss.
Near-resonant periodic driving of quantum systems promises the implementation of a large variety of novel quantum states, though their preparation and measurement remains challenging. We address these aspects in a model system consisting of interacting fermions in a periodically driven array of double wells created by an optical lattice. The singlet and triplet fractions and the double occupancy of the Floquet states are measured and their behavior as a function of the interaction strength is analyzed in the high- and low-frequency regimes. We demonstrate full control of the Floquet state population and find suitable ramping protocols and time scales that adiabatically connect the initial ground state to different targeted Floquet states. The micromotion that exactly describes the time evolution of the system within one driving cycle is observed. Additionally, we provide an analytic description of the model and compare it to numerical simulations.