Related papers: One-dimensional quasicrystals with power-law hoppi…
In the one-dimensional quasiperiodic Aubry-Andr\'{e}-Harper Hamiltonian with nearest-neighbor hopping, all single-particle eigenstates undergo a phase transition from ergodic to localized states at a critical disorder strength $W_c/t =…
In this paper, a non-Hermitian Aubry-Andr\'e-Harper model with power-law hoppings ($1/s^{a}$) and quasiperiodic parameter $\beta$ is studied, where $a$ is the power-law index, $s$ is the hopping distance, and $\beta$ is a member of the…
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…
Quasicrystals are fascinating and important because of their unconventional atomic arrangements, which challenge traditional notions of crystalline structures. Unlike regular crystals, they lack translational symmetry and generate unique…
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…
Localization in one-dimensional disordered or quasiperiodic non-interacting systems in presence of power-law hopping is very different from localization in short-ranged systems. Power-law hopping leads to algebraic localization as opposed…
We introduce and explore a family of self-dual models of single-particle motion in quasiperiodic potentials, with hopping amplitudes that fall off as a power law with exponent $p$. These models are generalizations of the familiar…
We investigate a generalized Aubry-Andr\'{e}-Harper (AAH) model with non-reciprocal hopping and power-law quasiperiodic potentials $V(i) = V\left[ \cos(2\pi \beta i) \right]^p$. Our study reveals that the interplay between nonreciprocity,…
Pair localization in one-dimensional quasicrystals with nearest-neighbor hopping is independent of whether short-range interactions are repulsive or attractive. We numerically demonstrate that this symmetry is broken when the hopping…
We study a non-Hermitian AA model with long-range hopping, $1/r^a$, and different choices of quasiperiodic parameters $\beta$ to be a member of the metallic mean family. We find that when the power-law exponent is in the $a<1$ regime, the…
We develop a theoretical scheme to perform a read-out of the properties of a quasi-periodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a 1D…
The present work discusses the possibility to realize correlated disorder in electrical circuits and studies the localization phenomena in terms of two-port impedance. The correlated disorder is incorporated using the Aubry-Andr\'{e}-Harper…
We study the effects of superconducting $p$-wave pairing on the non-Hermitian Aubry-Andr\'e-Harper model with power-law hopping. For the case of short-range hopping, weak pairing leads to oscillating quasi-Majorana zero modes, turning to…
Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility…
In this paper, we explore the localization transition and the scaling properties of both quasi-one-dimensional and two-dimensional quasiperiodic systems, which are constituted from coupling several Aubry-Andr\'{e} (AA) chains along the…
We propose a general framework for constructing self-dual one-dimensional quasiperiodic lattice models with arbitrary-range hoppings and multifractal behaviors. Our framework generates a broad spectrum of one dimensional quasicrystals,…
We study the single-particle properties of two-dimensional quasicrystals where the underlying geometry of the tight-binding lattice is crystalline but the on-site potential is quasicrystalline. We will focus on the 2D generalised…
Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we…
We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground…
In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization…