Effects of impurity scattering in the one-dimensional quantum sine-Gordon system are investigated by the use of the fermion representation of boson fields. Treating the scattering of particles by an impurity we find that a single impurity gives rise to bound states in the energy gap of the corresponding fermion system.
The doped Mott insulator in one dimension has been studied based on the phase Hamiltonian with the Umklapp scattering process, in which the charge degree of freedom is described by the quantum sine-Gordon model. The well-known equivalence between the quantum sine-Gordon model and the massive Thirring model for the spinless fermion makes it clear that the Mott-Hubbard gap originates from the Umklapp scattering process as was indicated by Emery and Giamarchi. Compressibility, density-density correlation function, frequency dependence of optical conductivity and Drude weight have been calculated in the presence of the impurity scattering treated in the self-consistent Born approximation. It is seen that there exists a crossover behavior in the spectral weight of charge excitations: the acoustic mode is dominant in small wave number region while the optical excitations across the Mott-Hubbard gap lie in large wave number region and that this crossover wave number is reduced as the Mott transition is approached.
The dynamical behavior of the one-dimensional quantum sine-Gordon system with a misfit parameter is investigated at a particular value of the quantum parameter g2=4π. For this purpose the dynamical correlation functions are calculated by using the Fermi-Bose relation. From the behavior of the displacement correlation function we find that the thermal velocity is given by ∼√T/m0 in the commensurate state (m0-| µ 8730|≫T) or in the cross-over region (m0≃| µ \tilde |≫T) and approaches value 1 as T or | µ \tilde | is increased. Here m0 and µ \tilde, respectively, are the gap and the chemical potential in the corresponding fermion system. For the case of denity-density correlation function, we give in the commensurate state expressions which are similar to those derived on the basis of the soliton phenomenology in the classical system. A particular case of the density-density correlation function is discussed in detail by following another route.