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-$\frac{1}{2}$ XXZ chain, we demonstrate that the current density at special values of the anisotropy parameter $\mathrm{\ensuremath{\Delta}}=\ensuremath{-}cos(\ensuremath{\pi}/p)$ $(p=3,4,5,\ensuremath{\cdots})$ in the ferromagnetic gapless regime behaves qualitatively the same as in the noninteracting case $(\mathrm{\ensuremath{\Delta}}=0)$ even in the weak electric field limit. When $\mathrm{\ensuremath{\Delta}}$ 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.
Highlights
Imagine a system of electrons in a one-dimensional (1D) ring [Fig. 1(a)]
Our study is complementary to the previous work [16] which discussed a different electric field regime for the infinite system by the generalized hydrodynamics method
The energy density ε(t ) and the current density j(t ) of the time-dependent problem are fully characterized by the adiabatic ground-state energy density εAGS(A) of the timeindependent system. This immediately implies the possibility of Bloch oscillations even under an infinitesimal electric field for the special values = − cos(π /p) (p = 2, 3, . . . ), where the period A = 2π /(p − 1) of εAGS(A) remains nonzero in the large L limit
Summary
Imagine a system of electrons in a one-dimensional (1D) ring [Fig. 1(a)]. Suppose that a static and uniform electric field E is turned on at time t = 0. Electrons keep accelerated and the induced electric current density increases linearly as a function of time, i.e., j(t ) D1Et. In the presence of a disorder-free lattice with the lattice constant a, on the other hand, noninteracting electrons get accelerated initially but start to move backward [Fig. 1(b)], forming an oscillatory motion. Similar divergence has been observed in noninteracting systems in the presence of a localized impurity [12] These results imply that the Bloch oscillations in noninteracting and imperfection-free systems may completely disappear when interactions or disorders are added. This is the case for a tight-binding model with a single defect in the limit of the weak electric field [12]. Our study is complementary to the previous work [16] which discussed a different electric field regime for the infinite system by the generalized hydrodynamics method
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