Coexistence of ergodic and weakly ergodic states in finite-height Wannier-Stark ladders

Abstract

We investigate a single-particle in one-dimensional Wannier-Stark ladders with either a linear potential or a mosaic potential with spacing $\kappa =2$. In both cases, we exactly determine the critical energies separating the weakly ergodic states from ergodic states for a finite potential height. Especially in the latter case, we demonstrate a rich phase diagram with ergodic states, weakly ergodic states, and strongly Wannier-Stark localized states. Our results also exhibit that critical energies are highly dependent on the height of the ladder and ergodic states only survive at $E\approx 0$ for the high ladder. Importantly, we find that the number of ergodic states can be adjusted by changing the interval of the non-zero potential. These interesting features will shed light on the study of disorder-free systems.

arXiv comment10 pages, 12 figures, accepted by physical review A

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• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
• Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
• Reentrant localization transition induced by a composite potential
• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
• Bound states in one-dimensional systems with colored noise
• Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices