2-PARTICLE FLUCTUATIONS IN ONE-DIMENSIONAL GENERALIZED LANDAU LIQUIDS

We use the Landau-liquid character of the low-energy eigenstate spectrum of the Hubbard chain in a magnetic field to investigate its two-particle spectral properties. The picture that emerges is that of a gas of two coupled fluids of pseudoparticles. The kinetic equations that govern the flow of pseudoparticles are derived. The macroscopic currents are expressed in terms of the elementary pseudoparticle currents. As a central result we evaluate in the limit of zero momentum the wave function for the electronic excitations obtained by applying the up-spin and down-spin density-fluctuation operators on the ground state. This wave function is calculated on the basis of the pseudoparticle single-pair eigenstates. It is defined by the microscopic two-particle matrix elements of the corresponding fluctuations taken between the ground state and the elementary excitations. The on-site interaction U, electronic density n, and magnetic field H dependence of these matrix elements, which play a major role in the two-particle spectral functions, provide relevant information on the microscopic foundation of the one-dimensional Landau-liquid theory. This leads to the introduction of an adiabatic continuity principle, which is valid in the Hilbert subspace of the pseudoparticle single-pair eigenstates of lowest energy and momentum. The non-Landau-liquid character of the zero-magnetic-field Luttinger phase, where such an adiabatic continuity principle is not valid, is explained. Exact expressions for the two-pseudoparticle forward-scattering amplitudes and for the charge-charge and spin-spin correlation functions at small momentum and low frequency are obtained. The dependence of the charge and spin stiffnesses of the conductivity spectra on U, n, and H, which is determined by the pseudoparticle transport masses, is investigated in detail. The study of these masses and of the effective charge and spin projection of the pseudoparticles gives information on their structure in the electronic representation. It is shown that the decoupling that characterizes the low-energy excitation spectrum does not correspond in the case of finite magnetic fields to a real charge-spin separation. Our results provide a method for the study of the low-frequency dynamics of interacting systems solvable with the Bethe ansatz, and we identify the spectral parameters that control the non-classical critical exponents with microscopic two-electron matrix elements.