Spectral density of the Hubbard-model by the continued fraction method

TL;DR

This paper introduces a continued fraction method (CFM) for calculating the spectral density of the Hubbard model, effectively capturing the entire spectral range and quasiparticle energy scales without phenomenological parameters.

Contribution

The paper develops a novel CFM with complex coefficients and a terminator function, enabling accurate spectral density calculations in the Hubbard model across different regimes.

Findings

Results agree with dynamical mean field theory variants

Method is free of phenomenological parameters

Applicable to strong coupling and near metal-insulator transition

Abstract

We present the continued fraction method (CFM) as a new microscopic approximation to the spectral density of the Hubbard model in the correlated metal phase away from half filling. The quantity expanded as a continued fraction is the single particle Green function. Leading spectral moments are taken into account through a set of real expansion coefficients, as known from the projection technique. The new aspect is to add further stages to the continued fraction, with complex coefficients, thus defining a terminator function. This enables us to treat the entire spectral range of the Green function on equal footing and determine the energy scale of the Fermi liquid quasiparticles by minimizing the total energy. The solution is free of phenomenological parameters and remains well defined in the strong coupling limit, near the doping controlled metal-insulator transition. Our results for the density of states agree reasonably with several variants of the dynamical mean field theory. The CFM requires minimal numerical effort and can be generalized in several ways that are interesting for applications to real materials.