Fermion loops, loop cancellation and density correlations in two dimensional Fermi systems

Details Fermion loops, loop cancellation and density correlations in two dimensional Fermi systems Fermion loops, loop cancellation and density correlations in two dimensional Fermi systems

1998-05-18

arxiv.org/abs/cond-mat/9805207v2

Phys.Rev. B58 (1998) 15449

Physics

Condensed Matter

24 pages (including 3 EPS figures), LaTeX2e; submitted to Phys. Rev. B

Scientific paper

10.1103/PhysRevB.58.15449

We derive explicit results for fermion loops with an arbitrary number of density vertices in two dimensions at zero temperature. The 3-loop is an elementary function of the three external momenta and frequencies, and the N-loop can be expressed as a linear combination of 3-loops with coefficients that are rational functions of momenta and frequencies. We show that the divergencies of single loops for low energy and small momenta cancel each other when loops with permuted external variables are summed. The symmetrized N-loop, i.e. the connected N-point density correlation function of the Fermi gas, does not diverge for low energies and small momenta. In the dynamical limit, where momenta scale to zero at fixed finite energy variables, the symmetrized N-loop vanishes as the (2N-2)-th power of the scale parameter.

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