Stroboscopic versus non-stroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

TL;DR

This paper compares stroboscopic and non-stroboscopic dynamics in Floquet systems realizing the Harper-Hofstadter Hamiltonian, showing non-stroboscopic methods better capture the full evolution of observables.

Contribution

It demonstrates that non-stroboscopic dynamics accurately reflect the Floquet Hamiltonian for all observables, unlike stroboscopic dynamics which are limited to commuting observables.

Findings

Non-stroboscopic dynamics capture the evolution of any observable.

Stroboscopic dynamics only match high-frequency limit for commuting observables.

Finite-frequency corrections are analyzed through numerical simulations.

Abstract

We study the stroboscopic and non-stroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian. We show that the former produces the evolution expected in the high-frequency limit only for observables which commute with the operator to which the driving protocol couples. On the contrary, non-stroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the density operator following a quantum cyclotron orbit on a $2\times 2$ plaquette, as well as the chiral current operator flowing along the legs of a $2\times 20$ ladder. The exact evolution is compared with its stroboscopic and non-stroboscopic counterparts, including finite-frequency corrections.