Phases of two coupled Luttinger liquids

TL;DR

This paper analyzes a model of two coupled Luttinger liquids, revealing phases with massless bosons, critical sectors, and spin gaps, and discusses implications for crossover to Fermi liquid behavior in multi-chain systems.

Contribution

It provides exact results for coupled Luttinger liquids with various interactions, including the identification of phases and critical behavior, extending understanding of one-dimensional fermion systems.

Findings

Presence of two massless boson sectors for forward scattering

Existence of an Ising-type critical sector

Dominance of spin excitation gap and pairing fluctuations in general interactions

Abstract

A model of two interacting one--dimensional fermion systems (``Luttinger liquids'') coupled by single--particle hopping is investigated. Bosonization allows a number of exact statements to be made. In particular, for forward scattering only, the model contains two massless boson sectors and an Ising type critical sector. For general interactions, there is a spin excitation gap and either s-- or d--type pairing fluctuations dominate. It is shown that the same behavior is also found for strong interactions. A possible scenario for the crossover to a Fermi liquid in a many chain system is discussed.