Simulating lattice fermion doubling with a Floquet drive

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.

Figures (1)

• Figure 1: In the leftmost panel, we plot the quasienergy eigenvalues with respect to crystal momenta $k$ for the singly driven (top) and doubly driven (bottom) cases. The center panel plots the eigenvalues of the target Hamiltonian on the discrete-time side. The Hamiltonian and eigenvalues of the two cases are identical. The right panel shows the solutions to the discrete-time equation of motion that reproduce the Floquet quasienergy eigenvalues from the left panel, again in both the singly driven (top) and doubly driven (bottom) cases. The plots correspond to parameter values $t_0 = \frac{\pi}{4}$, $t_1 = (1.1) \frac{\pi}{4}$, i.e., we have picked a gapped region of the spectra to illustrate the equivalence.