2000/04/27 by Behnam Farid, Farid, Behnam
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.cond-mat/0004476
36 pages, 3 figures included
arxiv created 2000/04/27 · openalex publication_date 2000/04/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For uniform systems of spin-less fermions in d spatial dimensions with d > 1, interacting through the isotropic two-body potential v(r-r'), a celebrated theorem due to Luttinger (1961) states that under theassumption_ of validity of the many-body perturbation theory the self-energy Sigma(k;epsilon), with 0 ,< epsilonF, with alphak >,= 0. As this is, by definition, specific to self-energies of Landau Fermi-liquid systems, treatment of non-Fermi-liquid systems are therefore thought to lie outside the domain of applicability of the many-body perturbation theory; that, for these systems, the many-body perturbation theory shouldnecessarily_ break down. We demonstrate that Im[Sigma(k;epsilon)] ~ -,+ alphak (epsilon-epsilonF)2, epsilon >,< epsilonF, isimplicit_ in Luttinger's proof and that, for d > 1, in principle nothing prohibits a non-Fermi-liquid-type (and, in particular Luttinger-liquid-type) Sigma(k;epsilon) from being obtained within the framework of the many-body perturbation theory. We in addition indicate how seemingly innocuous Taylor expansions of the self-energy with respect to k, epsilon or both amount to tacitly assuming that the metallic system under consideration is a Fermi liquid, whether the self-energy is calculated perturbatively or otherwise. Proofs that a certain metallic system is in a Fermi-liquid state, based on such expansions, are therefore tautologies.