Related papers: The almost mobility edge in the almost Mathieu equ…
We consider a simple model of an electron moving in a T-shaped confinement potential. This model allows for an analytical solution that explicitly demonstrates the existence of laterally bound electron states in quantum wires obtained by…
Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree-Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave…
We revisit the problem of an elastic line (e.g. a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension $d=1+1$. Upon applying a transverse field, a delocalization transition is expected, beyond…
We present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction $U$ and (ii) the…
The von Neumann entropy for an electron in periodic, disorder and quasiperiodic quantum small-world networks(QSWNs) are studied numerically. For the disorder QSWNs, the derivative of the spectrum averaged von Neumann entropy is maximal at a…
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…
Non-Hermitian quasicrystals possess PT and metal-insulator transitions induced by gain and loss or nonreciprocal effects. In this work, we uncover the nature of localization transitions in a generalized Aubry-Andre-Harper model with…
We study the Hubbard model on the AB-stacked bilayer honeycomb lattice with a repulsive onsite interaction U in second order perturbation theory and in self-consistent random phase approximation. We determine the changes in the…
We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works…
Quantum transport properties of electron systems driven by strong electric fields are studied by mapping the Landau-Zener transition dynamics to a quantum walk on a semi-infinite one-dimensional lattice with a reflecting boundary, where the…
A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wavefunction for two electrons occupying the same Wannier orbital…
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…
We study spinless fermions on a finite chain with nearest-neighbor repulsion and in the presence of a Wannier-Stark linearly-varying electric field potential. In the absence of the interaction, the eigenstates are localized for the system's…
Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility---ultimately signalling…
Robust edge transport can occur when particles in crystalline lattices interact with an external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge…
Materials featuring touching points, localized states, and flat bands are of great interest in condensed matter and artificial systems due to their implications in topology, quantum geometry, superconductivity, and interactions. In this…
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 investigate a one-dimensional tight-binding model in which onsite potentials $\{\varepsilon_i\}$ exhibit power-law spatial correlations (with exponent $\alpha$) and the hopping amplitudes decay as $t_{ij}\sim |i-j|^{-\beta}$. This…
We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-Andr\'e-Harper(AAH) model with power-law hoppings ($\sim \frac{1}{r^\sigma}$) when the quasiperiodicity parameter is chosen to be a member of…
For a class of discrete quasi-periodic Schroedinger operators defined by covariant re- presentations of the rotation algebra, a lower bound on phase-averaged transport in terms of the multifractal dimensions of the density of states is…