Duality in Power-Law Localization in Disordered One-Dimensional Systems

X. Deng 1 V. e. Kravtsov 2, 3 G. v. Shlyapnikov 4, 5, 6, 7, 8 L. Santos 1

Physical Review Letters, American Physical Society, 2018, 120 (11), 〈10.1103/PhysRevLett.120.110602〉

The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of $a>0$. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops ($a<1$) and short-range hops ($a>1$) in which the wave function amplitude falls off algebraically with the same power $\gamma$ from the localization center.

• 1. LUH - Leibniz Universität Hannover [Hannover]
• 2. ICTP - International Center for Theoretical Physics [Trieste]
• 3. L.D. Landau Institute for Theoretical Physics of RAS
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 5. SPEC - UMR3680 - Service de physique de l'état condensé
• 6. Russian Quantum Center
• 7. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
• 8. Wuhan Institute of Physics and Mathematics