Bloch oscillations in the spin-1/2 XXZ chain

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.

8 pages, 7 figures

References in corpus (5)

• The Luttinger liquid and integrable models
• Nonlinear current response of an isolated system of interacting fermions
• Insulator, conductor and commensurability: a topological approach
• Fine structure of the nonlinear Drude weights in the spin-1/2 XXZ chain
• Adiabatic transport in one-dimensional systems with a single defect

Cited by in corpus (4)

• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Fine structure of the nonlinear Drude weights in the spin-1/2 XXZ chain
• Two-doublon Bloch oscillations in the mass-imbalanced extended Fermi-Hubbard model
• Drude weights in one-dimensional systems with a single defect