Exponentially localized Wannier functions in periodic zero flux magnetic fields

Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields

Tight frames of exponentially decaying Wannier functions

Let L be a Schrödinger operator ( i ∂ ∂x −A(x))2+V (x) with periodic magnetic and electric potentials A,V , a Maxwell operator ∇× 1 ε(x)∇× in a periodic medium, or an arbitrary self-adjoint elliptic linear partial differential operator in R with coefficients periodic with respect to a lattice Γ. Let also S be a finite part of its spectrum separated by gaps from the rest of the spectrum. We cons...

Maximally localized Wannier functions for GW quasiparticles

We review the formalisms of the self-consistent GW approximation to many-body perturbation theory and of the generation of optimally localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave functions from such GW calculations can be used within this Wannier framework. These Wannier functions can be used to interpolate the many-body band structure from t...

Maximally-localized Wannier functions in perovskites: Cubic BaTiO3

The electronic ground state of a periodic crystalline solid is usually described in terms of extended Bloch orbitals; localized Wannier functions can alternatively be used. These two representations are connected by families of unitary transformations, carrying a large degree of arbitrariness. We have developed a localization algorithm that allows one to iteratively transform the extended Bloch...

Wannier Functions for Lattices in a Magnetic Field Ii: Extension to Irrational Fields

This paper extends earlier work on the definition of Wannier functions for Bloch electrons in a magnetic field. Extensions to irrational as well as rational magnetic fields are defined, and their properties investigated. The results are used to give a generalisation of the Peierls effective Hamiltonian which is valid when the magnetic flux per unit cell is close to any rational number. * Addres...