Susceptibility and vertex corrections for a square Fermi surface

TL;DR

This paper analytically examines the susceptibility of a nested square Fermi surface, revealing sharp peaks, divergence at low temperatures, and the impact of vertex corrections, with implications for high-Tc superconductivity theories.

Contribution

It provides explicit formulas for susceptibility and vertex corrections in nested Fermi systems, highlighting their effects on spin fluctuations and instabilities.

Findings

Imaginary susceptibility peaks scale with frequency over temperature.

Vertex corrections significantly modify RPA susceptibility.

Particle-hole symmetry causes diagram cancellations at half filling.

Abstract

We investigate the response of an electron system which exhibits ideal nesting features. Using the standard Matsubara formalism we 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 frequency divided by temperature. The peak lineshapes resemble neutron scattering data on chromium and some copper oxide superconductors. The real part of the bare susceptibility at the nesting vectors diverges logarithmically at low temperatures. Analytic formulas 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. We discuss the consequences of these results for spin fluctuation theories of high temperature superconductors and spin density wave instabilities.