A Luttinger's theorem revisited
| dc.creator | Farid, Behnam | |
| dc.date | 2000-04-27 | |
| dc.date.accessioned | 2026-07-07T02:37:29Z | |
| dc.date.available | 2026-07-07T02:37:29Z | |
| dc.description | 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 the_assumption_ of validity of the many-body perturbation theory the self-energy Sigma(k;epsilon), with 0 <,= k <,~ 3 k_F (where k_F stands for the Fermi wavenumber), satisfies the following universal asymptotic relation as epsilon approaches the Fermi energy epsilon_F: Im[Sigma(k;epsilon)] ~ -,+ alpha_k (epsilon-epsilon_F)^2, epsilon >,< epsilon_F, with alpha_k >,= 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 should_necessarily_ break down. We demonstrate that Im[Sigma(k;epsilon)] ~ -,+ alpha_k (epsilon-epsilon_F)^2, epsilon >,< epsilon_F, is_implicit_ 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. | |
| dc.description | 36 pages, 3 figures included | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0004476 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0004476 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/16307 | |
| dc.subject | Strongly Correlated Electrons | |
| dc.title | A Luttinger's theorem revisited | |
| dc.type | text |