Algebraic localization in disordered one-dimensional systems with long-range hopping.
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 prove that in one-dimensional systems all eigenstates remain algebraically 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 ($a>1$) that exhibit the same localization properties.
Publisher URL: http://arxiv.org/abs/1706.04088