Quantum Levy flights and multifractality of dipolar excitations in a random system

X. Deng 1 B. L. Altshuler 2, 3 G. V. Shlyapnikov 4, 2, 5, 6, 7 L. Santos 1

Physical Review Letters, American Physical Society, 2016, 117, pp.020401

We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). We analyze the eigen-energy spectra and the multifractal structure of the wavefunctions. In 1D and 2D all states are localized, although in 2D the localization length can be extremely large leading to an effective localization-delocalization crossover in realistic systems. In 3D all eigenstates are extended but not always ergodic, and we identify the energy intervals of ergodic and non-ergodic states. The reduction of the lattice filling induces an ergodic to non-ergodic transition, and the excitations are mostly non-ergodic at low filling.

  • 1. LUH - Leibniz Universität Hannover [Hannover]
  • 2. Kavli Institute for Theoretical Physics
  • 3. Columbia University [New York]
  • 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 5. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
  • 6. Russian Quantum Center
  • 7. Wuhan Institute of Physics and Mathematics