Susceptibility and vertex corrections for a square Fermi surface

The authors investigate the response of an electron system which exhibits ideal nesting features. Using the standard Matsubara formalism they derive analytic expressions for the imaginary and real parts of the bare particle-hole susceptibility. The imaginary part has sharp peaks whose maxima at the nesting momenta approximately scale with (ω/T). The peak lineshapes resemble neutron scattering data on chromium and some copper oxide superconductors. The real part of the bare susceptibility at the nestling vectors diverges logarithmically at low temperatures. Analytic formulae for the first vertex correction to the susceptibility are derived for a Hubbard interaction and its momentum and temperature variations are calculated numerically. This term detracts substantially from the ordinary RPA terms for intermediate values of the Coulomb repulsion. Exact cancellation of a certain class of diagrams at half filling is shown to result from particle-hole symmetry. They discuss the consequences of these results for spin fluctuation theories of high temperature superconductors and spin density wave instabilities