Abstract
Mapping the one-dimensional Hubbard model into the Luttinger-Tomonaga model, we have calculated the temperature dependencies of the chain copper nuclear magnetic spin-lattice relaxation rate and Knight shift for the normal state of the superconducting materials ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}.$ The dynamic spin susceptibility has been obtained by using a bosonization technique and results of the renormalization group analysis for one-dimensional quantum systems. A comparison of our results with experiment shows that the model is able to reproduce the main features of the spin dynamics in both materials.
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