Charge and spin response functions for the Tomonaga model with quadratic dispersion and different interactions
We derive expressions for the charge and spin response function for the Tomonaga model with quadratic dispersion and arbitrary (but finite for zero momentum) interaction. For constant interaction these expressions are analytic and for other types of interaction only a simple matrix has to be diagonalised. We use a truncated expansion in particle-hole states with and without inclusion of correlations in the ground state yielding an exact result for pure intra-band interaction. We also discuss the possibility of power-laws in the dynamic structure factor for the spinful and spinless model.