The Existence of Generalised Wannier Functions for One-Dimensional Systems

1998 ◽  
Vol 190 (3) ◽  
pp. 541-548 ◽  
Author(s):  
A. Nenciu ◽  
G. Nenciu
Keyword(s):  
Wannier Functions ◽  
One Dimensional

scholarly journals Universality of Abelian and non-Abelian Wannier functions in generalized one-dimensional Aubry-André-Harper models

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Kiryl Piasotski ◽  
Mikhail Pletyukhov ◽  
Clara S. Weber ◽  
Jelena Klinovaja ◽  
Dante M. Kennes ◽  
...  
Keyword(s):  
Wannier Functions ◽  
One Dimensional

Wannier functions and the calculation of localized modes in one-dimensional photonic crystals

2018 ◽  
Vol 35 (4) ◽  
pp. 826 ◽  
Author(s):  
Maria C. Romano ◽  
Arianne Vellasco-Gomes ◽  
Alexys Bruno-Alfonso
Keyword(s):  
Photonic Crystals ◽  
Localized Modes ◽  
Wannier Functions ◽  
One Dimensional

scholarly journals One-dimensional ballistic transport with FLAPW Wannier functions

2012 ◽  
Vol 85 (24) ◽  
Author(s):  
Björn Hardrat ◽  
Neng-Ping Wang ◽  
Frank Freimuth ◽  
Yuriy Mokrousov ◽  
Stefan Heinze
Keyword(s):  
Ballistic Transport ◽  
Wannier Functions ◽  
One Dimensional

scholarly journals Engineering spectral properties of non-interacting lattice Hamiltonians

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Ali Moghaddam ◽  
Dmitry Chernyavsky ◽  
Corentin Morice ◽  
Jasper van Wezel ◽  
Jeroen van den Brink
Keyword(s):  
Spectral Properties ◽  
Tight Binding ◽  
Integral Form ◽  
Higher Dimensions ◽  
Exact Diagonalization ◽  
Wannier Functions ◽  
One Dimensional ◽  
Binding Models ◽  
Bounded Functions ◽  
Position Dependence

We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

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