Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

TL;DR

This paper investigates the maximum group velocity in a one-dimensional Floquet system with a sinusoidally varying staggered potential, revealing conditions for dynamical localization and particle spreading behaviors.

Contribution

It combines numerical and analytical methods to analyze the maximum group velocity in a driven 1D model, applying Floquet theory, adiabatic, Magnus, and perturbation approaches.

Findings

Dynamical localization occurs when the maximum group velocity vanishes.

Maximum group velocity influences light cone spreading of particles.

Different regimes are characterized by the relative magnitude of the potential and hopping.

Abstract

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low frequency limit we use adiabatic theory, while in the high frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an "engineered" initial state where the particles (taken to be hard core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light cone like spreading of the particles in real space.