188 research outputs found
Reduction formula for fermion loops and density correlations of the 1D Fermi gas
Fermion N-loops with an arbitrary number of density vertices N > d+1 in d
spatial dimensions can be expressed as a linear combination of (d+1)-loops with
coefficients that are rational functions of external momentum and energy
variables. A theorem on symmetrized products then implies that divergencies of
single loops for low energy and small momenta cancel each other when loops with
permuted external variables are summed. We apply these results to the
one-dimensional Fermi gas, where an explicit formula for arbitrary N-loops can
be derived. The symmetrized N-loop, which describes the dynamical N-point
density correlations of the 1D Fermi gas, does not diverge for low energies and
small momenta. We derive the precise scaling behavior of the symmetrized N-loop
in various important infrared limits.Comment: 14 pages, to be published in Journal of Statistical Physic
Parametrization of Nambu vertex in a singlet superconductor
We analyze general properties of the effective Nambu two-particle vertex and
its renormalization group flow in a spin-singlet superconductor. In a fully
spin-rotation invariant form the Nambu vertex can be expressed by only three
distinct components. Solving exactly the flow of a mean-field model with
reduced BCS and forward scattering interactions, we gain insight into the
singularities in the momentum and energy dependences of the vertex at and below
the critical energy scale for superconductivity. Using a decomposition of the
vertex in various interaction channels, we manage to isolate singular momentum
and energy dependences in only one momentum and energy variable for each term,
such that the singularities can be efficiently parametrized.Comment: 21 pages, 5 figure
Fermi Surface of the 2D Hubbard Model at Weak Coupling
We calculate the interaction-induced deformation of the Fermi surface in the
two-dimensional Hubbard model within second order perturbation theory. Close to
half-filling, interactions enhance anisotropies of the Fermi surface, but they
never modify the topology of the Fermi surface in the weak coupling regime.Comment: 4 pages, LaTeX2e, 5 embedded EPS figures, accepted to be published in
Z. Phys.
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