Spectral density of the Hubbard model by the continued fraction method

Abstract

We present the continued fraction method (CFM) as a 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’s function. Leading spectral moments are taken into account through a set of real expansion coefficients, as known from the projection technique. Further stages are added to the continued fraction, with complex coefficients, thus defining a terminator function. This enables us to treat the entire spectral range of the Green’s 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 those from 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.