The Fermi Liquid as a Renormalization Group Fixed Point: the Role of Interference in the Landau Channel
نویسندگان
چکیده
We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action’s interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zeroangle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid. 71.10.Ay, 71.27.+a, 11.10.Hi, 05.30.Fk Typeset using REVTEX 1
منابع مشابه
The Fermi Liquid as a Renormalization Group Fixed Point
par Guennadi Chitov Thèse présentée au département de Physique en vue de l'obtention du grade de Docteurès sciences (Ph. SUMMARY The renormalization-group (RG) method is applied to study interacting fermions at finite temperature. A model based on the ψ 4-Grassmann effective action with SU(N)-invariant short-range interaction and a rotationally invariant Fermi surface in spatial dimensions d = ...
متن کاملNon-Fermi-Liquid Behavior and Anomalous Suppression of Landau Damping in Layered Metals Close to Ferromagnetism.
We analyze the low-energy physics of nearly ferromagnetic metals in two spatial dimensions using the functional renormalization group technique. We find a new low-energy fixed point, at which the fermionic (electronlike) excitations are non-Fermi-liquid (z_{f}=13/10) and the magnetic fluctuations exhibit an anomalous Landau damping whose rate vanishes as Γ_{q}∼|q|^{3/5} in the low-|q| limit. We...
متن کاملFermi liquid theory: a renormalization group point of view
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 Γ in the limit of small momentum (Q) and energy (Ω) transfer and obtain the equation which determines the collective modes of a Fermi ...
متن کاملRenormalization group for non-relativistic fermions
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus w...
متن کاملRenormalization Group Approach to Interacting Fermions
The stability or lack thereof of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group (RG) framework, in close analogy with the study of critical phenomena using φ scalar field theory. A brief introduction to φ theory in four dimensions and the path integral formulation for fermions is given before turning to the problem at hand. As for the latter, the f...
متن کامل