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

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron

Magnetic phase diagram of Sr3Fe2O7-delta

Magnetometry, electrical transport, and neutron scattering measurements were performed on single crystals of the Fe4+-containing perovskite-related phase Sr3Fe2O7−δ as a function of oxygen content. Although both the crystal structure and electron configuration of this compound are closely similar to those of well-studied ruthenates and manganates, it exhibits very different physical properties. The fully oxygenated compound (δ=0) exhibits a charge-disproportionation transition at TD=340 K, and an antiferromagnetic transition at TN=115 K. For temperatures T≤TD, the material is a small-gap insulator; the antiferromagnetic order is incommensurate, which implies competing exchange interactions between the Fe4+ moments. The fully deoxygenated compound (δ=1) is highly insulating, and its Fe3+ moments exhibit commensurate antiferromagnetic order below TN∼600 K. Compounds with intermediate δ exhibit different order with lower TN, likely as a consequence of frustrated exchange interactions between Fe3+ and Fe4+ sublattices. A previous proposal that the magnetic transition temperature reaches zero is not supported. © 2013, American Physical Society