Bloch oscillations in the spin-1/2 XXZ chain

TL;DR

This paper investigates Bloch oscillations in the strongly interacting spin-1/2 XXZ chain, revealing conditions under which the oscillations resemble noninteracting cases and how they are suppressed when parameters deviate.

Contribution

It demonstrates that at specific anisotropy values, the XXZ chain exhibits Bloch oscillations similar to noninteracting particles, extending understanding of these phenomena in strongly correlated systems.

Findings

Oscillations occur at special anisotropy values $\, ext{Delta}=- ext{cos}( ext{pi}/p)$.

Amplitude suppression when $ ext{Delta}$ deviates from these values.

Estimated electric field strength for observing oscillations using Landau--Zener formula.

Abstract

Under a perfect periodic potential, the electric current density induced by a constant electric field may exhibit nontrivial oscillations, so-called Bloch oscillations, with an amplitude that remains nonzero in the large system size limit. Such oscillations have been well studied for nearly noninteracting particles and observed in experiments. In this work, we revisit Bloch oscillations in strongly interacting systems. By analyzing the spin-1/2 XXZ chain, which can be mapped to a model of spinless electrons, we demonstrate that the current density at special values of the anisotropy parameter $\Delta=-\cos(\pi/p)$ ($p=3,4,5,\cdots$) in the ferromagnetic gapless regime behaves qualitatively the same as in the noninteracting case ($\Delta=0$) even in the weak electric field limit. When $\Delta$ deviates from these values, the amplitude of the oscillation under a weak electric field is suppressed by a factor of the system size. We estimate the strength of the electric field required to observe such a behavior using the Landau--Zener formula.