Stochastic diagonalization of Hamiltonian: a genetic algorithm-based approach

Abstract

We propose and demonstrate the workability of a genetic-algorithm-based technique of finding the eigenvalues and eigenfunctions of a real symmetric Hamiltonian matrix. The algorithm can be tailored to extract all the eigenvalues at a time or to extract only the lowest or the highest eigenvalue first and then sequentially determine the next few higher (lower) eigenvalues. The algorithm is generalized to handle diagonalization problems in which the basis functions themselves are optimized simultaneously. Several model applications are reported.