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.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.

Physical review. B, Condensed matterMar 15, 199385 citations

Chiral Tomonaga-Luttinger Liquids and the Calogero-Sutherland Model with Boundaries

Yamamoto, Takashi, Norio Kawakami, Sung-Kil Yang

Applying boundary conformal field theory we study the low-energy critical behavior of the Calogero-Sutherland model of $BC_N$ -type. The universality class of the model is found to be a {\it chiral} Tomonaga-Luttinger liquid. Various correlation exponents depending on the interaction strength are obtained.Applying boundary conformal field theory we study the low-energy critical behavior of the Calogero-Sutherland model of $BC_N$-type. The universality class of the model is found to be a {\it chiral} Tomonaga-Luttinger liquid. Various correlation exponents depending on the interaction strength are obtained.

arXiv:cond-mat/9512078Dec 11, 19950 citations

The Conductivity of the Tomonaga‐Luttinger Model

Victor Bârsan

physica status solidi (b)Jun 1, 19890 citations

Tomonaga-Luttinger Anomalous Exponents of k F , 3 k F , 5 k F and 7 k F Momentum Distribution in the t-J Model

Nelson Oyindenyifa Nenuwe, J. O. A. Idiodi

Contrary to the usual Fermi liquids, where the exponent of the momentum distribution at k=kF is fixed to an integer, for the Tomonaga-Luttinger (TL) liquids the anomalous exponent of the momentum distribution changes continuously, resulting in a power-law singularity of the momentum distribution function. It has been said that this power-law singularity appears at kF and 3kF for the Hubbard model as well as at kF for the t-J model. Using the conformal field theory (CFT) technique, we present an exact calculation of the anomalous exponent of the t-J model at kF, 3kF, 5kF and 7kF and compare it with the results for the Hubbard model.Contrary to the usual Fermi liquids, where the exponent of the momentum distribution at k=kF is fixed to an integer, for the Tomonaga-Luttinger (TL) liquids the anomalous exponent of the momentum distribution changes continuously, resulting in a power-law singularity of the momentum distribution function. It has been said that this power-law singularity appears at kF and 3kF for the Hubbard model as well as at kF for the t-J model. Using the conformal field theory (CFT) technique, we present an exact calculation of the anomalous exponent of the t-J model at kF, 3kF, 5kF and 7kF and compare it with the results for the Hubbard model.

American Journal of Condensed Matter PhysicsJan 1, 20150 citations

Functional‐Integral Treatment of the Disordered Tomonaga‐Luttinger Model

P. Kleinert

physica status solidi (b)Oct 1, 19891 citation

Applying boundary conformal field theory we study the low-energy critical behavior of the Calogero-Sutherland model of

BC_N

-type. The universality class of the model is found to be a {\it chiral} Tomonaga-Luttinger liquid. Various correlation exponents depending on the interaction strength are obtained.