‘‘Luttinger-liquid’’ behavior of the normal metallic state of the 2D Hubbard model

Abstract

Analysis of interacting fermion systems shows that there are two fundamentally different fixed points, Fermi-liquid theory and ‘‘Luttinger-liquid theory’’ (Haldane), a state in which charge and spin acquire distinct spectra and correlations have unusual exponents. The Luttinger liquids include most interacting one-dimensional systems, and some higher- (especially two) dimensional systems in which the band spectrum is bounded above, systems with Mott-Hubbard gaps and an upper Hubbard band. We give a theory which is useful in calculating normal-state, and some superconducting, properties of high-${\mathit{T}}_{\mathit{c}}$ superconductors.