A Density Matrix-based Algorithm for Solving Eigenvalue Problems

TL;DR

The paper introduces FEAST, a novel density matrix-based algorithm for symmetric eigenvalue problems, inspired by quantum mechanics, demonstrating high efficiency, robustness, and scalability in electronic structure calculations.

Contribution

It presents a fundamentally different eigenvalue solver from traditional methods, leveraging contour integration and density matrices for improved performance.

Findings

High efficiency and robustness demonstrated on parallel architectures

Accurate results in electronic structure calculations of Carbon nanotubes

Scalable performance for large eigenvalue problems

Abstract

A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, and takes its inspiration from the contour integration and density matrix representation in quantum mechanics. It will be shown that this new algorithm - named FEAST - exhibits high efficiency, robustness, accuracy and scalability on parallel architectures. Examples from electronic structure calculations of Carbon nanotubes (CNT) are presented, and numerical performances and capabilities are discussed.