Related papers: Emergent criticality in the Aubry-Andr\'e model wi…
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 argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moir\'e materials, which make large flux per unit cell…
We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-Andr\'{e} model. By analyzing the Lyapunov exponent and localization length, we…
Aubry-Andre Harper (AAH) lattice models, characterized by reflection-asymmetric, sinusoidally varying nearest-neighbor tunneling profile, are well-known for their topological properties. We consider the fate of such models in the presence…
We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr\'{e} model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and…
We study the combined effect of quasiperiodic disorder, driven and interaction in the periodically kicked Aubry-Andr\'{e} model. In the non-interacting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a…
Quasi-periodic Schr\"odinger-type operators naturally arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the…
We study the interplay of superconductivity and a wide spectrum of critical (multifractal) wave functions ("spectrum-wide quantum criticality," SWQC) in the one-dimensional Aubry-Andr\'e and power-law random-banded matrix models with…
We investigate topological phenomena in a spatially modulated Dirac-$\delta$ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy…
Topological quantum optical states in one-dimensional (1D) quasiperiodic cold atomic chains are studied in this work. We propose that by introducing incommensurate modulations on the interatomic distances of 1D periodic atomic chains, the…
Quantum criticality in systems of local moments interacting with itinerant electrons has become an important and diverse field of research. Here we review recent results which concern (a) quantum phase transitions in single-impurity Kondo…
Off-diagonal Aubry-Andr\'{e} (AA) model has recently attracted a great deal of attention as they provide condensed matter realization of topological phases. We numerically study a generalized off-diagonal AA model with p-wave superfluid…
Non-Hermitian effects could create rich dynamical and topological phase structures. In this work, we show that the collaboration between lattice dimerization and non-Hermiticity could generally bring about mobility edges and multiple…
We investigate localization in a quasiperiodically engineered diamond lattice with strand-dependent Aubry-Andr\'e-Harper onsite modulations, highlighting the decisive roles of the modulation ratio $s$ and the averaged potential on the…
Quasiperiodic systems are neither randomly disordered nor translationally invariant in the absence of periodic length scales. Based on their incommensurate order, novel physical properties such as critical states and self-similar…
In this paper, we study the critical behaviors in the non-Hermitian disorder Aubry-Andr\'{e} (DAA) model, and we assume the non-Hermiticity is introduced by nonreciprocal hopping. We employ the localization length $\xi$, the inverse…
We study one-dimensional optical lattices described by generalized Aubry-Andr\'e models that include both commensurate and incommensurate modulations of the hopping amplitude. This brings together two interesting features of this class of…
In this paper, we explore the localization features of wave functions in a family of mosaic quasiperiodic chains obtained by continuously interpolating between two limits: the mosaic Aubry-Andr\'{e} (AA) model, known for its exact mobility…
We discuss a two-dimensional system under the perturbation of a Moire potential, which takes the same geometry and lattice constant as the underlying lattices but mismatches up to relative rotation. Such a self-dual model belongs to the…
We study a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of triangular and dual honeycomb lattice sites. In the classical ground state the spins on different sublattices are decoupled, but quantum…