Fermi liquid theory: a renormalization group point of view
Abstract
We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a twodimensional system with a circular Fermi surface, we derive RG equations at oneloop order for the twoparticle 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 densitydensity 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 $limit of the twoparticle vertex function (${\Gamma ^\Omega }^*$). We show how the results obtained at oneloop order can be extended to all orders in a loop expansion. Calculating the quasiparticle lifetime and renormalization factor at twoloop order, we reproduce the results obtained from twodimensional bosonization or Ward Identities. We discuss the zerotemperature limit of the RG equations and the difference between the Field Theory and the KadanoffWilson formulations of the RG. We point out the importance of $n$body ($n\geq 3$) interactions in the latter.
 Publication:

arXiv eprints
 Pub Date:
 April 1996
 arXiv:
 arXiv:condmat/9604189
 Bibcode:
 1996cond.mat..4189D
 Keywords:

 Condensed Matter
 EPrint:
 33 pages (RevTex), 5 poscript figures