Related papers: The driven Harper model
We construct useful sets of one-particle states in the quantum Hall system based on the von Neumann lattice. Using the set of momentum states, we develop a field-theoretical formalism and apply the formalism to the system subjected to a…
We consider the Hartree equation for infinitely many electrons with a constant external magnetic field. For the system, we show a local well-posedness result when the initial data is the pertubation of a Fermi sea, which is a non-trace…
We study the effects of a periodically driven electric field applied to a variety of tight-binding models in one dimension. We first consider a non-interacting system with or without a staggered on-site potential, and we find that that…
We extensively study the localization and the quantum Hall effect in the Hofstadter butterfly, which emerges in a two-dimensional electron system with a weak two-dimensional periodic potential. We numerically calculate the Hall conductivity…
We study localization properties of electronic states in one-dimensional lattices with nearest-neighbour interaction. Both the site energies and the hopping amplitudes are supposed to be of arbitrary form. A few cases are considered in…
We have derived a new set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is…
We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential and focus on paramagnetic effects of the external magnetic field. The Hamiltonian considered consists of…
We consider the change in electron localization due to the presence of electron-electron repulsion in the \HA model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an…
We derive the field correction to the Berry curvature of Bloch electrons, which can be traced back to a positional shift due to the interband mixing induced by external electromagnetic fields. The resulting semiclassical dynamics is…
Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…
The Kronig-Penney model describes what happens to electron states when a confining potential is repeated indefinitely. This model uses a square well potential; the energies and eigenstates can be obtained analytically for a the single well,…
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 investigate a celebrated problem of one dimensional tight binding model in the presence of disorder leading to Anderson localization from a novel perspective. A binary disorder is assumed to be created by immobile heavy particles for the…
We discuss the consequences of including both electron-phonon and electron-electron couplings in multi-band models, focusing on numerical studies of a one-dimensional two-band model in the intermediate regime for both coupling strengths.…
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the…
We consider local magnetic moments coupled to conduction electrons with on-site attraction, in order to discuss the interplay between pairing and magnetic order. We probe the ground state properties of this model on a one-dimensional…
We study localization and charge dynamics in a monochromatically driven one-dimensional Anderson insulator focussing on the low-frequency, strong-driving regime. We study this problem using a mapping of the Floquet Hamiltonian to a hopping…
We analyze the quantum transport properties of MAPbI3 within a tight-binding model. Charge carriers are strongly scattered by the Fr\"ohlich interaction with longitudinal optical phonon modes. This limits their mobilities at room…
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time.…