Continuous renormalization for fermions and Fermi liquid theory
نویسنده
چکیده
I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the recursive equation for the Green functions, and thus improves the combinatorial behaviour. The form of the equation is also ideal for the investigation of manyfermion systems, where the propagator is singular on a surface. For these systems, I define a criterion for Fermi liquid behaviour which applies at positive temperatures. As a first step towards establishing such behaviour in d ≥ 2, I prove basic regularity properties of the interacting Fermi surface to all orders in a skeleton expansion. The proof is a considerable simplification of previous ones.
منابع مشابه
Renormalization by Continuous Unitary Transformations: One-Dimensional Spinless Fermions
A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the hamiltonian which stays hermitian throughout the renormalization flow, whereby any frequency dependence is avoided. The approach is illustrated in detail for a model of spin...
متن کاملInteracting Fermi liquid in two dimensions at finite temperature Part II: Renormalization
Abstract This is a companion paper to [DR1]. Using the method of continuous renormalization group around the Fermi surface and the results of [DR1], we achieve the proof that a two-dimensional jellium system of interacting Fermions at low temperature T is a Fermi liquid above the BCS temperature Following [S1], this means proving analyticity in the coupling constant λ for |λ|| logT | ≤ K where ...
متن کاملOne-dimensional fermions with neither Luttinger-liquid nor Fermi-liquid behavior.
It is well known that, generically, one-dimensional interacting fermions cannot be described in terms of a Fermi liquid. Instead, they present a different phenomenology, that of a Tomonaga-Luttinger liquid: the Landau quasiparticles are ill defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine tuning of the interaction between fermions c...
متن کاملRG on a Fermi surface
We review the renormalization group (RG) method for interacting fermions, building off typical φ theory to account for the presence of a Fermi surface. A few geometries and the general procedure are briefly discussed. The method is illustrated with a model of two Fermi circles with different spin components and momenta, which can describe experiments with interacting fermions. General results o...
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