Rafael Antonio Lainez Reyes

arXiv2026

Diagonalization of the Landau Hamiltonian with a Periodic Potential via a Galerkin Projection Method and Applications to Topological Band Properties

In this paper, we study the numerical computation of eigenfunctions of the Landau Hamiltonian with a periodic potential. We propose a spectral method using the eigenfunctions of the Landau operator that allows us to numerically compute the band structure for potentials of different strengths, including the well-studied weak and strong potentials, and additionally systems in the intermediate regime. We then apply the method to simulations across the full range of coupling constants from weak to strong coupling and present an analysis of the band structure as a function of the potential strength.

physics.comp-ph↗

arXiv2025

Fully guaranteed and computable error bounds on the energy for periodic Kohn-Sham equations with convex density functionals

In this article, we derive fully guaranteed error bounds for the energy of convex nonlinear mean-field models. These results apply in particular to Kohn-Sham equations with convex density functionals, which includes the reduced Hartree-Fock (rHF) model, as well as the Kohn-Sham model with exact exchange-density functional (which is unfortunately not explicit and therefore not usable in practice). We then decompose the obtained bounds into two parts, one depending on the chosen discretization and one depending on the number of iterations performed in the self-consistent algorithm used to solve the nonlinear eigenvalue problem, paving the way for adaptive refinement strategies. The accuracy of the bounds is demonstrated on a series of test cases, including a Silicon crystal and an Hydrogen Fluoride molecule simulated with the rHF model and discretized with planewaves. We also show that, although not anymore guaranteed, the error bounds remain very accurate for a Silicon crystal simulated with the Kohn-Sham model using nonconvex exchangecorrelation functionals of practical interest.

math.NA↗