Springer LINK: The European Physical Journal B - Abstract Volume 3 Issue 3 (1998) pp 315-331

The European Physical Journal B

ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)

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Abstract Volume 3 Issue 3 (1998) pp 315-331

Fermi liquid theory: a renormalization group approach

N. Dupuis (a)

Department of Physics, University of Maryland, College Park, MD 20742-4111, USA

Received: 27 June 1997 / Received in final form: 17 December 1997 / Accepted: 26 January 1998

Abstract: 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 $\Gamma $in the limit of small momentum (${\bf Q}$) and energy ($\Omega $) 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 F_l^s and F_l^a) is determined by the fixed point value of the $\Omega $-limit of the two-particle vertex function (${\Gamma ^\Omega }^*$). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of n-body ($n\geq 3$) 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

(a) On leave from Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France; email: dupuis@glue.umd.edu

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