Physica B Condensed Matter

Luttinger-liquid parameter of Hubbard chain and Hubbard ladder models in the Hartree–Fock approximation

Kazuhiro Sano

Published Jun 1, 2000• 2 citations

DOI: 10.1016/s0921-4526(99)00879-0

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Physica B Condensed Matter

Luttinger-liquid parameter of Hubbard chain and Hubbard ladder models in the Hartree–Fock approximation

Kazuhiro Sano

Published Jun 1, 2000• 2 citations

Publisher

DOI: 10.1016/s0921-4526(99)00879-0

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arXiv:2209.02361Reports on Mathematical PhysicsOct 1, 20231 citation

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Luttinger-Liquid Parameter of Hubbard Chain and Hubbard Ladder

Kazuhiro Sano

We study the Luttinger-liquid parameter $K_ρ$ of the Hubbard chain and the Hubbard ladder models by the ordinary perturbation method combined with the Luttinger-liquid relation. According to the Luttinger-liquid relation, the critical exponent $K_ρ$ is related to the charge susceptibility $χ_c$ and the Drude weight D by $ K\sbρ={1/2}(πχ_c D)^{1/2}$. By calculating these quantities with the perturbation method, we obtain $K_ρ$ at the first-order analytically and up to the second-order numerically. We compare these results with results of the Bethe ansatz for the Hubbard chain and that of the numerical diagonalization for the Hubbard ladder. It shows that the perturbation calculation of $K_ρ$ is reliable in the weak coupling regime.We study the Luttinger-liquid parameter $K_ρ$ of the Hubbard chain and the Hubbard ladder models by the ordinary perturbation method combined with the Luttinger-liquid relation. According to the Luttinger-liquid relation, the critical exponent $K_ρ$ is related to the charge susceptibility $χ_c$ and the Drude weight D by $ K\sbρ={1/2}(πχ_c D)^{1/2}$. By calculating these quantities with the perturbation method, we obtain $K_ρ$ at the first-order analytically and up to the second-order numerically. We compare these results with results of the Bethe ansatz for the Hubbard chain and that of the numerical diagonalization for the Hubbard ladder. It shows that the perturbation calculation of $K_ρ$ is reliable in the weak coupling regime.

arXiv:cond-mat/9912128Journal of the Physical Society of JapanApr 15, 20008 citations

The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties

G. Jüttner, A. Klümper, J. Suzuki

arXiv:cond-mat/9711310Nuclear Physics BJul 1, 199890 citations

We study the Luttinger-liquid parameter

K_ρ

of the Hubbard chain and the Hubbard ladder models by the ordinary perturbation method combined with the Luttinger-liquid relation. According to the Luttinger-liquid relation, the critical exponent

K_ρ

is related to the charge susceptibility

χ_c

and the Drude weight D by $ K\sbρ={1/2}(πχ_c D)^{1/2}$. By calculating these quantities with the perturbation method, we obtain

K_ρ

at the first-order analytically and up to the second-order numerically. We compare these results with results of the Bethe ansatz for the Hubbard chain and that of the numerical diagonalization for the Hubbard ladder. It shows that the perturbation calculation of

K_ρ

is reliable in the weak coupling regime.