Deng X, Kravtsov V E, Shlyapnikov G V, Santos L
Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany.
Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.
Phys Rev Lett. 2018 Mar 16;120(11):110602. doi: 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 γ from the localization center.
