Luttinger-liquid Parameter of Hubbard Chain and Hubbard Ladder

TL;DR

This paper calculates the Luttinger-liquid parameter $K_{\rho}$ for Hubbard models using perturbation methods and compares results with exact solutions, confirming reliability in weak coupling regimes.

Contribution

It introduces a perturbation-based approach to evaluate $K_{\rho}$ and validates its accuracy against Bethe ansatz and numerical diagonalization results.

Findings

Perturbation method yields reliable $K_{\rho}$ in weak coupling.

First-order analytical and second-order numerical results are consistent.

Comparison confirms validity of perturbation approach for Hubbard models.

Abstract

We study the Luttinger-liquid parameter $K_{\rho}$ 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 $K_{\rho}$ is related to the charge susceptibility $\chi_c$ and the Drude weight D by $ K\sb{\rho}={1/2}(\pi \chi_c D)^{1/2}$. By calculating these quantities with the perturbation method, we obtain $K_{\rho}$ 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 $K_{\rho}$ is reliable in the weak coupling regime.