Order in coupled metallic chains

Abstract

We consider a model of the quasi-one-dimensional conductors in which the electrons propagate on a lattice of identical metallic chains. The intrachain interactions are g₁, 9₂, and 9₄ and the interchain interactions are v₁, v₂, and v₄. The calculations are carried out for g₁=0 and g₁/πv_F = −6/5, which corresponds to the Luttinger and Luther-Emery lines. When only low-momentum transfer interchain interactions are considered, there is no phase transition. With interchain backscattering, the system may undergo a charge density wave phase transition, but no other type of phase transition. In particular, there cannot be a superconducting phase transition at a finite temperature without some interchain hopping. When interchain tunnelling processes are included, all types of possible long range orderings are possible, and the system undergoes a phase transition of the type which for the particular values of the intrachain interactions, the purely one-dimensional response function is the most divergent as T → 0.