Abstract
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.
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Grote, I., Körding, E. & Wegner, F. Stability Analysis of the Hubbard Model. Journal of Low Temperature Physics 126, 1385–1409 (2002). https://doi.org/10.1023/A:1013804405357
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DOI: https://doi.org/10.1023/A:1013804405357