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. This summary article contains the statements of the main results. The proofs are contained in the full, electronic, article. Electronic Supplementary Material: Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00220-004-1038-2.
Single Scale Analysis of Many Fermion Systems Part 4
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.
An intrinsic 1/N expansion for many-Fermion systems
The 1/N expansion is a popular tool for investigating non-perturbative long-range phenomena. In many-body models, discretization of the Fermi surface naturally introduces a many-component picture. If, for example, number symmetry is broken, N ≈ (exp [1/λ])(d-1), where λ > 0 is the bare coupling constant. We expect that this intrinsic 1/N expansion appears whenever the "free propagator" of the system is singular along a hypersurface (for instance, in the Anderson model for localized and extended states).