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 In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem.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

The performance of semi-quantitative differential PCR is similar to that of real-time PCR for the detection of the MYCN gene in neuroblastomas

Amplification of the MYCN gene in neuroblastomas is a potent biological marker of highly aggressive tumors, which are invariably fatal unless sound clinical management is applied. To determine the usefulness of semi-quantitative differential PCR (SQ-PCR) for accurate quantification of MYCN gene copy number, we evaluated the analytical performance of this method by comparing the results obtained with it for 101 tumor samples of neuroblastoma to that obtained by absolute and relative real-time PCR. Similar results were obtained for 100 (99%) samples, no significant difference was detected between the median log10 MYCN copy number (1.53 by SQ-PCR versus 1.55 by absolute real-time PCR), and the results of the two assays correlated closely (r = 0.8, Pearson correlation; P < 0.001). In the comparison of SQ-PCR and relative real-time PCR, SQ-PCR versus relative real-time PCR concordant results were found in 100 (99%) samples, no significant difference was found in median log10 MYCN copy number (1.53 by SQ-PCR versus 1.27 by relative real-time PCR), and the results of the two assays correlated closely (r = 0.8, Pearson correlation; P < 0.001). These findings indicate that the performance of SQ-PCR was comparable to that of real-time PCR for the amplification and quantification of MYCN copy number. Thus, SQ-PCR can be reliably used as an alternative assay in laboratories without facilities for real-time PCR