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One-dimensional quasi-periodic systems with power-law hopping, $1/r^a$, differ from both the standard Aubry-Azbel-Harper (AAH) model and from power-law systems with uncorrelated disorder. Whereas in the AAH model all single-particle states undergo a transition from ergodic to localized at a critical quasi-disorder strength, short-range power-law hops with $a>1$ can result in mobility edges. Interestingly, there is no localization for long-range hops with $aleq 1$, in contrast to the case of uncorrelated disorder. Systems with long-range hops are rather characterized by ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but non ergodic) states. We show that both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.
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 s
We show that in the regime when strong disorder is more relevant than field quantization the superfluid--to--Bose-glass criticality of one-dimensional bosons is preceded by the prolonged logarithmically slow classical-field renormalization flow of th
Non-interacting spinless electrons in one-dimensional quasicrystals, described by the Aubry-Andr{e}-Harper (AAH) Hamiltonian with nearest neighbour hopping, undergoes metal to insulator transition (MIT) at a critical strength of the quasi-periodic po
We study a non-Hermitian AA model with the long-range hopping, $1/r^a$, and different choices of the quasi-periodic parameters $beta$ to be the member of the metallic mean family. We find that when the power-law exponent is in the $a<1$ regime, the s
We numerically study spin transport and nonequilibrium spin-density profiles in a clean one-dimensional spin-chain with long-range interactions, decaying as a power-law,$r^{-alpha}$ with distance. We find two distinct regimes of transport: for $alpha