Luttinger liquids in higher dimensions

Abstract

One-dimensional chains arranged into a many-dimensional mesh are analyzed. The model is used to study the relevance of strong forward- and backward-scattering processes in systems that look isotropic over large scales. The model combines Luttinger- and Fermi-liquid features, depending on the position in the Fermi surface. Over most of it, Luttinger behavior prevails, although, at isolated points in the Brillouin zone, finite quasiparticle peaks exist.