Deng X, Ray S, Sinha S, Shlyapnikov G V, Santos L
Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany.
Indian Institute of Science Education and Research, Kolkata, Mohanpur, Nadia 741246, India.
Phys Rev Lett. 2019 Jul 12;123(2):025301. doi: 10.1103/PhysRevLett.123.025301.
One-dimensional quasiperiodic systems with power-law hopping, 1/r^{a}, differ from both the standard Aubry-André (AA) model and from power-law systems with uncorrelated disorder. Whereas in the AA model all single-particle states undergo a transition from ergodic to localized at a critical quasidisorder strength, short-range power-law hops with a>1 can result in mobility edges. We find that there is no localization for long-range hops with a≤1, in contrast to the case of uncorrelated disorder. Systems with long-range hops rather present ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but nonergodic) states. Both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.
具有幂律跳跃（1/r^a）的一维准周期系统，与标准的奥布里 - 安德烈（AA）模型以及具有不相关无序的幂律系统都不同。在AA模型中，所有单粒子态在临界准无序强度下会经历从遍历到局域化的转变，而当a>1时的短程幂律跳跃会导致迁移率边缘。我们发现，与不相关无序的情况相反，对于a≤1的长程跳跃不存在局域化。具有长程跳跃的系统反而呈现遍历到多重分形边缘以及从遍历到多重分形（扩展但非遍历）态的相变。迁移率边缘和遍历到多重分形边缘在膨胀动力学实验中都可能清晰地展现出来。
