Related papers: A numerical study of the localization transition o…
We study localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-Andr\'e model with an additional $N$th-neighbor hopping term of strength $J_{N}$. This long-range tunneling couples successive windings of an…
A recent experiment by P. Bordia et al. (Periodically Driving a Many Body Localized Quantum System, Nat Phys, Jan 2017) has demonstrated that periodically modulating the potential of a localised many-body quantum system described by the…
We present a thorough pedagogical analysis of the single particle localization phenomenon in a quasiperiodic lattice in one dimension. Description of disorder in the lattice is represented by the Aubry-Andr\'e model. Characterization of…
We study the finite size scaling of the bulk polarization in a quasiperiodic (Aubry-Andr\'{e}) model using the geometric analog of the Binder cumulant. As a proof of concept we show that the geometric Binder cumulant method described here…
The Aubry-Andr\'e 1D lattice model describes a particle hopping in a pseudo-random potential. Depending on its strength $\lambda$, all eigenstates are either localized ($\lambda>1$) or delocalized ($\lambda<1$). Near the transition, the…
We investigate a generalized interpolating Aubry-Andr\'{e}-Fibonacci (IAAF) model with p-wave superconducting pairing. In the Aubry-Andr\'{e} limit, we demonstrate that the system experiences transitions from a pure phase, either extended…
The Aubry-Andr\'e-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value $V_c$ of the quasiperiodic potential…
The localization of waves in non-periodic media is a universal phenomenon, occurring in a variety of different quantum and classical systems, including condensed-matter, Bose-Einstein condensates in optical lattices, quantum chaotic…
We study the localization transitions for coupled one-dimensional lattices with quasiperiodic potential. Besides the localized and extended phases there is an intermediate mixed phase which can be easily explained decoupling the system so…
Anderson localization is a phase transition between a metallic phase, where wavefunctions are extended and delocalized in space, and an insulating phase, where wavefunctions are completely localized. These transitions are driven by…
In this study, we investigate the localization transition and quantum criticality {in the ground state of the} disordered Aubry-Andr\'{e}-Harper (AAH) model, where a quasiperiodic potential is hybridized with a disordered potential. In the…
Although random matrix theory provides a fundamental framework for characterizing quantum chaos, encompassing both ergodic and localized phases, a comprehensive understanding of the universal features governing the critical transition…
We study the influence of many-particle interactions on a metal-insulator transition. We consider the two-interacting-particle problem for onsite interacting particles on a one-dimensional quasiperiodic chain, the so-called Aubry-Andr\'{e}…
Here we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of many-body localized phase at…
The front dynamics in the Harper (or Aubry-Andr\'e) model (which has a localization transition) is investigated using two different settings, particle number front where the system is at zero temperature, and initially, the particle numbers…
We show the localization transition and its effect on two dynamical processes for an extended Aubry-Andr\'e-Harper model with incommensurate on-site and hopping potentials. After specifying an extended Aubry-Andr\'e-Harper model, we check…
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 the localization and topological transitions in a one-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is described by a generalized Aubry-Andr\'{e}-Harper model with irrational modulations in the…
We study a generalized Aubry-Andre model that obeys $\mathcal{PT}$-symmetry. We observe a robust $\mathcal{PT}$-symmetric phase with respect to system size and disorder strength, where all eigenvalues are real despite the Hamiltonian being…
We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasi-periodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical…