One-dimensional Hubbard model in a magnetic field and the multicomponent Tomonaga-Luttinger model

The one-dimensional Hubbard model in a magnetic field is equivalent under renormalization-group transformation to a multicomponent Tomonaga-Luttinger model. The mapping between the Coulomb repulsion U of the Hubbard model and the couplings of the Tomonaga-Luttinger model is obtained for aribitrary magnetic field h and band filling n from a comparison of the correlation function exponents. These quantities are calculated for the Hubbard model from the finite-size corrections to the excitation energies, since the assumption of conformal invariance relates them to the critical exponents. On the other hand, the correlation functions of the multicomponent Tomonaga-Luttinger model are determined by solving the exact equation of motion derived by the use of generalized Ward identities.