Crossover between Luttinger and Fermi-liquid behavior in weakly coupled metallic chains

We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi-liquid behavior as the interchain hopping $t_{\perp }$ is varied. Although in the physically interesting case of finite but small $t_{\perp }$ the quasiparticle residue does not vanish, the single-particle Green’s function exhibits the signature of Luttinger-liquid behavior (i.e., anomalous scaling and spin-charge separation) in a large intermediate parameter regime. Using realistic parameters, we find that the scaling behavior in this regime is characterized by an anomalous dimension of the order of unity, as suggested by recent experiments on quasi-one-dimensional conductors. Our calculation also gives insights into the approximations inherent in higher-dimensional bosonization; in particular, we show that the replacement of a curved Fermi surface by a finite number $M$ of flat patches can give rise to unphysical nesting singularities in the single-particle Green’s function, which disappear only in the limit $M\to \infty$ or if curvature effects are included. We also compare our approach with other methods. This work extends our recent letter [Phys. Rev. Lett. 74, 2997 (1995)].