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

Momentum distribution neark=3 kF in the Tomonaga-Luttinger model

Karlo Penc, Jenő Sólyom

In contrast to normal Fermi liquids, where the momentum distribution n(k) has a discontinuous jump at k= ${\mathit{k}}_{\mathit{F}}$ , in Luttinger liquids a power-law singularity appears in n(k). It was argued that this singularity shows up not only at ${\mathit{k}}_{\mathit{F}}$ but at 3 ${\mathit{k}}_{\mathit{F}}$ ,5 ${\mathit{k}}_{\mathit{F}}$ , . . . as well, and the anomaly exponent has been detemined for the one-dimensional Hubbard model using numerical methods or assuming conformal invariance. We present an exact calculation of the anomaly exponent for the Tomonaga-Luttinger model and compare it with the results for the Hubbard model.In contrast to normal Fermi liquids, where the momentum distribution n(k) has a discontinuous jump at k=${\mathit{k}}_{\mathit{F}}$, in Luttinger liquids a power-law singularity appears in n(k). It was argued that this singularity shows up not only at ${\mathit{k}}_{\mathit{F}}$ but at 3${\mathit{k}}_{\mathit{F}}$,5${\mathit{k}}_{\mathit{F}}$, . . . as well, and the anomaly exponent has been detemined for the one-dimensional Hubbard model using numerical methods or assuming conformal invariance. We present an exact calculation of the anomaly exponent for the Tomonaga-Luttinger model and compare it with the results for the Hubbard model.

Physical review. B, Condensed matterDec 15, 199116 citations

In contrast to normal Fermi liquids, where the momentum distribution n(k) has a discontinuous jump at k=

{\mathit{k}}_{\mathit{F}}

, in Luttinger liquids a power-law singularity appears in n(k). It was argued that this singularity shows up not only at

{\mathit{k}}_{\mathit{F}}

but at 3

{\mathit{k}}_{\mathit{F}}

{\mathit{k}}_{\mathit{F}}

, . . . as well, and the anomaly exponent has been detemined for the one-dimensional Hubbard model using numerical methods or assuming conformal invariance. We present an exact calculation of the anomaly exponent for the Tomonaga-Luttinger model and compare it with the results for the Hubbard model.