The Fermi gas model of one-dimensional conductors

TLDR

The paper reviews the Fermi gas model of one‑dimensional conductors. It examines exact solutions for special coupling constants, extends them to arbitrary couplings using renormalization‑group arguments, analyzes instabilities through response functions, relates the model to others, and generalizes it to coupled chains to describe quasi‑one‑dimensional systems. The study discusses the crossover from one‑dimensional to three‑dimensional behavior and the resulting types of ordering.

Abstract

Abstract The Fermi gas model of one-dimensional conductors is reviewed. The exact solutions known for particular values of the coupling constants in a single chain problem (Tomonaga model, Luther-Emery model) are discussed. Renormalization group arguments are used to extend these solutions to arbitrary values of the couplings. The instabilities and possible ground states are studied by investigating the behaviour of the response functions. The relationship between this model and others is discussed and is used to obtain further information about the behaviour of the system. The model is generalized to a set of coupled chains to describe quasi-one-dimensional systems. The crossover from one-dimensional to three-dimensional behaviour and the type of ordering are discussed.