Response Functions of Two-Coupled Chains of Tomonaga-Luttinger Liquids

TL;DR

This study investigates the response functions of two coupled Tomonaga-Luttinger chains, revealing how intrachain interactions influence spin and charge fluctuations, with implications for electron pairing mechanisms.

Contribution

It provides a detailed analysis of the dynamical response functions in coupled Luttinger liquids, highlighting the effects of repulsive interactions on spin and charge fluctuations.

Findings

Enhanced spin fluctuation at q_y=π due to repulsive interactions

Suppressed charge fluctuation at q_y=π at low energies

Potential for attractive electron pairing from spin fluctuations

Abstract

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