Charge and spin transport in the one-dimensional Hubbard model

We study the charge and spin currents transported by the elementary excitat ions of the one-dimensional (1D) Hubbard model and derive the corresponding current spectra. We present results both for finite-size systems and in th e thermodynamic limit. This includes finding the couplings of both the low- energy and finite-energy (string) excitations to external charge and spin p robes. At zero magnetic held the general structure of the charge-spin separ ation survives at all energy scales and the effective charges of both the l ow-energy and finite-energy charge excitations are studied as functions of the on-site Coulomb interaction U, electronic density n, and applied magnet ic field H. In some limits the effective charge of the low-energy excitatio ns equals that of the electrons, whereas that of the finite-energy charge-s tring excitations of rapidity length gamma is found to be 2 gamma times the electronic charge. At U = infinity the spin excitations do not contribute to spin transport, whereas the low-energy charge excitations feel an effect ive flux given by (phi N-up arrow(up arrow) - phi N-down arrow(down arrow)) /(N-up arrow + N-down arrow), where N-sigma is the number of electrons of s pin sigma and phi (sigma) is a spin-dependent flux. This reveals that at ze ro magnetic field and U = oo there is no spin transport, while at finite ma gnetic field the low-energy charge excitations also carry spin. In the U mu ch greater than t limit the spin is carried both by holons and spinons. Fin ally, we find that the charge- and spin-current spectra can be derived from a semi-classical approach.