https://doi.org/10.1007/s100510050318
Fermi liquid theory: a renormalization group approach
Department of Physics, University of Maryland, College Park, MD
20742-4111, USA
Corresponding author: a dupuis@glue.umd.edu
Received:
27
June
1997
Revised:
17
December
1997
Accepted:
26
January
1998
Published online: 15 June 1998
We show how Fermi liquid theory results can be systematically
recovered using a renormalization group (RG) approach. Considering a
two-dimensional system with a circular Fermi surface, we derive RG
equations at one-loop order for the two-particle vertex function 
in the limit of small momentum (
) and energy (
) transfer
and obtain the equation which determines the collective modes of a Fermi
liquid. The density-density response function is also calculated.
The Landau function (or, equivalently, the Landau parameters 
and
) is determined by the fixed point value of the -limit of
the two-particle vertex function (
). We show
how the results obtained at one-loop order can be extended to all orders in a
loop expansion. Calculating the quasi-particle life-time and renormalization
factor at two-loop order, we reproduce the results obtained from
two-dimensional bosonization or Ward Identities. We
discuss the zero-temperature limit of the RG equations and the difference
between the Field Theory and the Kadanoff-Wilson formulations of the RG. We
point out the importance of n-body (
) interactions in the latter.
PACS: 05.30.Fk – Fermion systems and electron gas / 71.10.Ay – Fermi-liquid theory and other phenomenological models / 71.10.Ca – Electron gas, Fermi gas
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
