Non-Fermi-liquid metals in low dimensions
C. Di Castro and S. Caprara (sergio.caprara@roma1.infn.it)
Istituto Nazionale per la Fisica della Materia, SMC and Unit` a di Roma 1,
and Dipartimento di Fisica, Universit` a di Roma “La Sapienza”,
Piazzale Aldo Moro, 2 – I-00185 Roma, Italy
Abstract. In low-dimensional metals the presence of massless excitations may lead to a
breakdown of the Landau Fermi-liquid description, which successfully applies to higher-
dimensional metals. This breakdown is mirrored by infrared divergences which plague the
perturbative treatment of models for low-dimensional metals, despite the fact that the metal-
lic phase is a stable liquid phase of the matter. However, the very condition of stability
of the system implies exact cancellations among the singular terms in the response func-
tions, controlled by additional Ward identities, which must be considered besides the standard
Ward identities related to the conservation of the total particle and spin density. The com-
bined use of renormalization group and of these Ward identities allows for the closure of
the renormalization-group equations, leading to the description of the asymptotic (infrared)
behavior of the low-dimensional metal.
Keywords: low-dimensional metals; non-Fermi-liquid systems
PACS: xxx
1. Introduction
The low-energy behavior of most interacting fermionic systems can be dis-
cussed within a small number of universality classes. This classification can
be understood if one imagines to derive the effective asymptotic theory by
means of an iterated elimination of the high-energy degrees of freedom within
a Wilson renormalization-group scheme [1]. This procedure selects few types
of dominant scattering processes near the Fermi surface [2, 3, 4, 5] and allows
for a full description of the low-energy behavior of the system in terms of
few parameters. For pure systems, and in the absence of symmetry breaking
(e.g., magnetism, superconductivity,...) two types of metallic phases are well
known: the “normal” Fermi-liquid phase in d =3 [6], and the “anomalous”
Luttinger-liquid phase in d =1 [2].
The breakdown of the Fermi-liquid theory has been claimed to be relevant
within many physical contexts. For instance, a number of experimental evid-
ences indicates that the metallic phase of high-temperature superconducting
cuprates is not a Fermi liquid [7]. These materials are insulating with antifer-
romagnetic long-range order when stoichiometric, and become metallic upon
chemical doping, which introduces charge carriers (holes, in most cases) in
the system. The cuprates are characterized by a strongly anisotropic crystal
structure, based on copper-oxygen planes intercalated with rare-earth slabs,
39
R. Fazio et al. (eds.), New Directions in Mesoscopic Physics, 39–66.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.