Application of the shift-invert Lanczos algorithm to a non-equilibrium Green function for transport problems

TL;DR

This paper demonstrates that the shift-invert Lanczos algorithm significantly reduces computational costs in non-equilibrium Green's function calculations for transport problems, enabling efficient analysis of large systems.

Contribution

The paper introduces the application of the shift-invert Lanczos method to non-equilibrium Green's functions, improving computational efficiency for large Hamiltonians.

Findings

Computation time reduced by a factor of 33 for a 66,103-dimensional Hamiltonian.

Effective application to both simple and realistic Hamiltonians.

Potential for broader use in many-body transport simulations.

Abstract

Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method can dramatically reduce the computational effort. We apply the method to two test problems, namely a simple model Hamiltonian and to a more realistic Hamiltonian for nuclear fission. For a Hamiltonian of dimension 66103 we find that the computation time is reduced by a factor of 33 compared to the direct calculation of the Green's function.