A Renormalisation Group Approach to the Hubbard Model
After the discovery of high temperature superconductors the two dimensional Hubbard model has attracted a lot of attention as a description of these materials. Intensive studies have revealed that indeed its phase diagram shows features known from high temperature superconductors. We study the two dimensional Hubbard model with the aid of exact renormalisation group equations. For this purpose we rewrite the purely fermionic theory in a form where bosonic fields mediate the interaction between fermions. A symmetry breaking condensate then manifests itself in a nonvanishing expectation value for one of these bosonic fields. However, the bosonisation precedure induces an arbitrariness in the couplings between fermions and bosons due to the possibility to perform Fierz transformations. This arbitrariness is mirrored in ambiguous mean field results. By properly taking into account the running of the couplings, the renormalisation group is able to restore the invariance under equivalent choices of initial couplings. By following the flow into the broken phase we show how one may reconcile the Mermin-Wagner theorem with the observation of an antiferromagnetic long range order at nonvanishing temperatures.
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