Response Functions of Two-Coupled Chains of Tomonaga-Luttinger Liquids
Properties of fluctuations in two chains of Tomonaga-Luttinger liquids coupled by the interchain hopping have been studied by calculating retarded response functions $χ^R_ρ (q_x,q_y;ω)$ for charge and $χ^R_{\p} (q_x,q_y;ω)$ for spin where $q_x$ and $q_y (=0$ or $π$) denote the longitudinal and transverse wave vector, respectively, and $ω$ is the frequency. We have found the notable fact that the repulsive intrachain interaction results in the clear enhancement of ${\rm{Im}}χ^R_\p (q_x,π;ω)$ and the suppression of ${\rm{Im}}χ^R_ρ(q_x,π;ω)$ at low energies. This result indicates the importance of the dynamical effect by the spin fluctuation with $q_y = π$ and small $ω$, which has a possibility to give rise to the attractive interaction for the electron pairing.