11 research outputs found
Single Scale Analysis of Many Fermion Systems. Part 4: Sector Counting
For a two dimensional, weakly coupled system of fermions at temperature zero,
one principal ingredient used to control the composition of the associated
renormalization group maps is the careful counting of the number of quartets of
sectors that are consistent with conservation of momentum. A similar counting
argument is made to show that particle-particle ladders are irrelevant in the
case of an asymmetric Fermi curve.Comment: 52 pages, 2 figure
Particle-Hole Ladders
A self contained analysis demonstrates that the sum of all particle-hole
ladder contributions for a two dimensional, weakly coupled fermion gas with a
strictly convex Fermi curve at temperature zero is bounded. This is used in our
construction of two dimensional Fermi liquids.Comment: 131 pages, 26 figure
Single Scale Analysis of Many Fermion Systems. Part 2: The First Scale
The first renormalization group map arising from the momentum space
decomposition of a weakly coupled system of fermions at temperature zero
differs from all subsequent maps. Namely, the component of momentum dual to
temperature may be arbitrarily large - there is no ultraviolet cutoff. The
methods of Part 1 are supplemented to control this special case.Comment: 45 page
Single Scale Analysis of Many Fermion Systems. Part 1: Insulators
We construct, using fermionic functional integrals, thermodynamic Green's
functions for a weakly coupled fermion gas whose Fermi energy lies in a gap.
Estimates on the Green's functions are obtained that are characteristic of the
size of the gap. This prepares the way for the analysis of single scale
renormalization group maps for a system of fermions at temperature zero without
a gap.Comment: 42 page