Method of spectral densities for the Hubbard model

Sergei G. Ovchinnikov, Elena I. Shneyder

Under the assumption of long-range antiferromagnetic order at low temperatures, the spectral functions and the density of states are calculated in the two-dimensional Hubbard model with half-filling in the Hubbard-I approximation. The results are compared with the data obtained using an exact numerical technique, namely, the quantum Monte Carlo method. The influence of hopping to the next-to-nearest neighbor on the formation of the electronic structure is considered.

Tsutomu Momoi

Johannes Maria Singer, T. Schneider, P. F. Meier

Masanori Kohno

The single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight transfer, and upper Hubbard band are explained in terms of spinons, holons, antiholons, and doublons. The Mott transition is characterized by the emergence of a gapless mode whose dispersion relation extends up to the order of hopping t (spin exchange J) in the weak (strong) interaction regime caused by infinitesimal doping.

R. Hayn, P. Lombardo, Konrad Matho

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.

Martin Letz, R.J. Gooding