Perturbation theory and the exchange interaction in the one-dimensional Hubbard model

Anja Grage

In this work the optical excitations in the one-dimensional extended Peierls-Hubbard model are studied. There are two competing interactions in this model, namely the Coulomb interaction and the Peierls interaction. The latter causes a dimerised lattice structure. To calculate the optical excitations perturbatively, one needs to identify the dominant interaction of the model. In the field-theoretical limit using different methods, such as a semiclassical approach, mean-field theory and the renormalisation group, one finds that it is the Peierls-interaction which dominates the system and therefore defines the starting point for perturbation theory. Rayleigh-Schrödinger perturbation theory is carried out up to second order in the weak Coulomb interaction for the ground-state energy and the one-particle gap. The singlet and triplet exciton gaps, i.e. charge and spin gap, are calculated using Wannier perturbation theory, two-step perturbation theory and Downfolding perturbation theory. All results are compared to results obtained by using the density-matrix renormalisation group approach (DMRG).

S. Pairault, David Sénéchal, A.–M. S. Tremblay

Thomas Pruschke

Carsten Honerkamp A, Daniel Rohe, Sabine Andergassen +1 more

We propose an interaction flow scheme that sums up the perturbation expansion of many-particle systems by successively increasing the interaction strength. It combines the unbiasedness of renormalization group methods with the simplicity of straightforward perturbation theory. Applying the scheme to fermions in one dimension and to the two-dimensional Hubbard model we find that at one-loop level and low temperatures there is ample agreement with previous one-loop renormalization group approaches. We furthermore present results for the momentum dependence of spin, charge, and pairing interactions in the two-dimensional Hubbard model.

Hiroshi Takano, Masuo Suzuki

B. Lorenz

Abstract Band models with intrasite (Hubbard) and intersite Coulomb interactions are treated in a cluster approximation taking into account the interactions and the transfer within clusters of sites rigorously. Between different clusters the interaction is decoupled in a mean field approximation and the transfer term is treated as a perturbation. The ground‐state energy of the one‐dimensional Hubbard model is calculated up to fourth order in the perturbation and is compared with other approximations and the exact result. In the one‐dimensional spinless fermion model the perturbation is treated without further approximations by solving Dyson's equation for the one‐particle Green's function. The order‐disorder transition in this model is discussed.