Order in coupled metallic chains
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/πvF = −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.
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