85 research outputs found
Continuous renormalization for fermions and Fermi liquid theory
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 many-fermion 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 ge 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.Comment: LaTeX, 3 eps figure
Self-energy flows in the two-dimensional repulsive Hubbard model
We study the two-dimensional repulsive Hubbard model by functional RG
methods, using our recently proposed channel decomposition of the interaction
vertex. The main technical advance of this work is that we calculate the full
Matsubara frequency dependence of the self-energy and the interaction vertex in
the whole frequency range without simplifying assumptions on its functional
form, and that the effects of the self-energy are fully taken into account in
the equations for the flow of the two-body vertex function. At Van Hove
filling, we find that the Fermi surface deformations remain small at fixed
particle density and have a minor impact on the structure of the interaction
vertex. The frequency dependence of the self-energy, however, turns out to be
important, especially at a transition from ferromagnetism to d-wave
superconductivity. We determine non-Fermi-liquid exponents at this transition
point.Comment: 48 pages, 18 figure
Eliashberg equations derived from the functional renormalization group
We describe how the fermionic functional renormalization group (fRG) flow of
a Cooper+forward scattering problem can be continued into the superconducting
state. This allows us to reproduce from the fRG flow the fundamental equations
of the Eliashberg theory for superconductivity at all temperatures including
the symmetry-broken phase. We discuss possible extensions of this approach like
the inclusion of vertex corrections.Comment: 9 pages, 4 figure
Renormalization group flows into phases with broken symmetry
We describe a way to continue the fermionic renormalization group flow into
phases with broken global symmetry. The method does not require a
Hubbard-Stratonovich decoupling of the interaction. Instead an infinitesimally
small symmetry-breaking component is inserted in the initial action, as an
initial condition for the flow of the selfenergy. Its flow is driven by the
interaction and at low scales it saturates at a nonzero value if there is a
tendency for spontaneous symmetry breaking in the corresponding channel. For
the reduced BCS model we show how a small initial gap amplitude flows to the
value given by the exact solution of the model. We also discuss the emergence
of the Goldstone boson in this approach.Comment: 30 pages, LaTeX, 8 figure
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