Stability analysis of the Hubbard model

An effective Hartree–Fock–Bogoliubov-type interaction is calculated for the Hubbard model in second order in the coupling by means of flow equations. A stability analysis is performed in order to obtain the transition into various possible phases.We find, that the second order contribution weakens the tendency for the antiferromagnetic transition. Apart from a possible antiferromagnetic transition the d-wave Pomeranchuk instability recently reported by Halboth and Metzner is usually the strongest instability. A newly found instability is of p-wave character and yields band-splitting. In the BCS-channel one obtains the strongest contribution for \(d_{x^2 - y^2 } \)-waves. Other types of instabilities of comparable strength are also reported.