Dynamical and spectral properties of low dimensional materials

This chapter follows its companion, chapter 1. Here we review different methods based on the Bethe ansatz solution of the one-dimensional Hubbard model, in order to study quantities related to charge transport and the momentum dependent conductivity. Moreover, we report recent developments on finite-energy dynamical properties. This is achieved by introducing new entities called pseudofermions which are basically free, in the sense that their energies are additive, and where the effect of the interactions appears through phase shifts that are absorbed by their discrete momentum values. The resulting pseudofermion dynamical theory enables the evaluation of matrix elements between energy eigen-states and hence the derivation of finite energy expressions for the one- and two-electron correlation and spectral functions. Comparison with experimental results is also discussed.