https://doi.org/10.1140/e10051-002-0009-7
Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities
1
Département de Physique, Université de Fribourg, Pérolles, 1700 Fribourg, Switzerland
2
Laboratoire de Physique de la Matière Condensée (CNRS UMR 8551) , École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France and
Laboratoire de Physique Théorique et Hautes Énergies (CNRS UMR 7589) , Universités Paris VII, 4 Place Jussieu, 75252 Paris Cedex 05, France
Corresponding author: a benedikt.binz@unifr.ch
Received:
11
April
2001
Revised:
6
September
2001
Published online: 15 January 2002
The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces.
PACS: 71.10.Fd – Lattice fermion models (Hubbard model, etc.) / 71.10.Hf – Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems / 74.72.-h – High-Tc compounds
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
