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

In the framework of a diagram technique for Hubbard operators, a perturbation theory is formulated that takes into account scale renormalization of anomalous vertices. For the one-dimensional Hubbard model with strong correlation and quarter-filled band this perturbation theory is used to calculate the exchange interaction in a dimerized chain as a function of the dimerization and the parameters of the model.