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 – Abdus Salam International Centre 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