Disorder-driven transition in a chain with power-law hopping

We study a one-dimensional (1D) system with a power-law quasiparticle dispersion alpha|k|(alpha) sgn k in the presence of a short-range-correlated random potential, and demonstrate that for alpha < 1/2 it exhibits a disorder-driven quantum phase transition with critical properties similar to those of the localization transition near the edge of the band of a semiconductor in high dimensions, as studied recently [Phys. Rev. Lett. 114, 166601 (2015); Phys. Rev. B 91, 035133 (2015)]. Despite the absence of localization in the considered 1D system, the disorder-driven transition manifests itself, for example, in a critical form of the disorder-averaged density of states. We confirm the existence of the transition by numerical simulations and find the critical exponents and the critical disorder strength as a function of a. The proposed system thus presents a convenient platform for numerical studies of the recently predicted unconventional high-dimensional localization effects and has the potential for experimental realizations in chains of ultracold atoms in optical traps.