Plane Wave Methods for Quantum Eigenvalue Problems of Incommensurate Systems
This addresses the computational challenge of modeling incommensurate materials, which are important in condensed matter physics but previously required costly supercell approximations.
The authors propose a novel algorithm for computing electronic structure eigenvalue problems of incommensurate systems using plane wave methods, avoiding large supercell approximations. Numerical results in 1D and 2D demonstrate reliability and efficiency.
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our algorithm directly discretizes the eigenvalue problem under the framework of a plane wave method. The emerging ergodicity and the interpretation from higher dimensions give rise to many unique features compared to what we have been familiar with in the periodic system. The numerical results of 1D and 2D quantum eigenvalue problems are presented to show the reliability and efficiency of our scheme. Furthermore, the extension of our algorithm to full Kohn-Sham density functional theory calculations are discussed.