On-the-fly exact diagonalization solver for quantum electronic models

TL;DR

This paper introduces a novel numerical method for efficiently solving large-scale quantum electronic Hamiltonian matrices by on-the-fly matrix regeneration, demonstrated on the Anderson impurity model within DMFT.

Contribution

The paper presents a new basis arrangement and on-the-fly matrix generation algorithm that enable solving extremely large Hamiltonian matrices without full storage.

Findings

Successfully solved a 2.4 billion dimension matrix in DMFT.

Implemented the method on a distributed memory cluster.

Achieved efficient partial diagonalization of large quantum Hamiltonians.

Abstract

We propose a distinct numerical approach to effectively solve the problem of partial diagonalization of the super-large-scale quantum electronic Hamiltonian matrices. The key ingredients of our scheme are the new method for arranging the basis vectors in the computer's RAM and the algorithm allowing not to store a matrix in RAM, but to regenerate it on-the-fly during diagonalization procedure. This scheme was implemented in the program, solving the Anderson impurity model in the framework of dynamical mean-field theory (DMFT). The DMFT equations for electronic Hamiltonian with 18 effective orbitals that corresponds to the matrix with the dimension of 2.4 * 10^9 were solved on the distributed memory computational cluster.