Fermi liquid features of the one-dimensional Luttinger liquid

TL;DR

This paper demonstrates that one-dimensional electron systems can be effectively described by Fermi-liquid theory, connecting it with the traditional Luttinger-liquid framework and establishing a correspondence between their parameters.

Contribution

It introduces a Fermi-liquid description for 1D systems, linking Landau and Haldane parameters, and bridges the gap between Fermi-liquid and Luttinger-liquid theories.

Findings

Retrieves known Luttinger-liquid results from 1D Fermi-liquid theory

Establishes correspondence between Landau and Haldane parameters

Analyzes dynamical correlation functions and impurity problems using conformal field theory

Abstract

We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Fermi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the 1D Fermi-liquid theory. Exact correspondence between the Landau parameters and Haldane parameters is established. The exponents of the dynamical correlation functions and the impurity problem are also discussed based on the finite size corrections of elementary excitations with the predictions of the conformal field theory, which provides a bridge between the 1D Fermi-liquid and the Luttinger liquid.