A Davidson-Lanczos iteration method for computation of continued-fraction expansion of the Green's function at very low temperatures: Applications to the dynamical mean field theory

TL;DR

This paper introduces a combined Davidson-Lanczos iterative method to efficiently compute the Green's function's continued fraction expansion at very low temperatures, improving calculations in dynamical mean field theory.

Contribution

It develops a novel hybrid approach combining Davidson and Lanczos algorithms for low-temperature Green's function calculations in many-body physics.

Findings

The method accurately reproduces results compared to full diagonalization.

It efficiently computes low-lying eigenvalues and Green's functions.

Application to Hubbard model demonstrates practical effectiveness.

Abstract

We present a combination method based on orignal version of Davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric Hamiltonian matrix and the simplest version of Lanczos technique for obtaining a tridiagonal representation of the Hamiltonian to compute the continued fraction expansion of the Green's function at a very low temperature. We compare the Davidson$+$Lanczos method with the full diagonalization on a one-band Hubbard model on a Bethe lattice of infinite-coordination using dynamical mean field theory.