Two-Particle-Self-Consistent Approach for the Hubbard Model

摘要: Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as Random Phase Approximation are no longer valid since they predict finite temperature antiferromagnetic phase transition prohibited by Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem well particle conservation, Pauli principle, local moment and charge sum rules. self-energy formula does not assume Migdal There is consistency between one- two-particle quantities. Internal accuracy checks allow one test limits of validity TPSC. Here I present pedagogical review TPSC along with short summary existing results case studies: a) opening pseudogap when correlation length larger than thermal de Broglie wavelength, b) conditions for appearance d-wave superconductivity two-dimensional model.