Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling

We present a general framework how to investigate stability of solutions within a single self-consistent renormalization scheme being a parquet-type extension of the Baym-Kadanoff construction of conserving approximations. To obtain a consistent description of one- and two-particle quantities, needed for the stability analysis, we impose equations of motion on the one- as well on the two-particle Green functions simultaneously and introduce approximations in their input, the completely irreducible two-particle vertex. Thereby we do not loose singularities caused by multiple two-particle scatterings. We find a complete set of stability criteria and show that each instability, singularity in a two-particle function, is connected with a symmetry-breaking order parameter, either of density type or anomalous. We explicitly study the Hubbard model at intermediate coupling and demonstrate that approximations with static vertices get unstable before a long-range order or a metal-insulator transition can be reached. We use the parquet approximation and turn it to a workable scheme with dynamical vertex corrections. We derive a qualitatively new theory with two-particle self-consistence, the complexity of which is comparable with FLEX-type approximations. We show that it is the simplest consistent and stable theory being able to describe qualitatively correctly quantum critical points and the transition from weak to strong coupling in correlated electron systems.Comment: REVTeX, 26 pages, 12 PS figure

Crossover from two- to three-dimensional critical behavior for nearly antiferromagnetic itinerant electrons

The crossover from two- to three-dimensional critical behavior of nearly antiferromagnetic itinerant electrons is studied in a regime where the inter-plane single-particle motion of electrons is quantum-mechanically incoherent because of thermal fluctuations. This is a relevant regime for very anisotropic materials like the cuprates. The problem is studied within the Two-Particle Self-Consistent approach (TPSC), that has been previously shown to give a quantitative description of Monte Carlo data for the Hubbard model. It is shown that TPSC belongs to the $n\rightarrow \infty$ limit of the $O\left( n\right)$ universality class. However, contrary to the usual approaches, cutoffs appear naturally in the microscopic TPSC theory so that parameter-free calculations can be done for Hubbard models with arbitrary band structure. A general discussion of universality in the renormalized-classical crossover from $d=2$ to $d=3$ is also given.Comment: Revtex, 23 pages + 6 postcript figures (with epsfile

Genomic profiling of late-onset basal cell carcinomas from two brothers with nevoid basal cell carcinoma syndrome.

Nevoid basal cell carcinoma syndrome (NBCCS) is an autosomal dominant genetic disorder. It is commonly caused by mutations in PTCH1 and chiefly characterized by multiple basal cell carcinomas (BCCs) developing prior to the age of 30 years. In rare cases, NBCCS presents with a late onset of BCC development. To investigate BCC tumorigenesis in two brothers, who showed characteristic features of NBCCS but developed their first BCCs only after the age of 40 years. Two other siblings did not show signs of NBCCS. We obtained blood samples from four siblings and nine BCCs from the two brothers with NBCCS. Whole exome sequencing and RNA sequencing revealed loss of heterozygosity (LOH) of PTCH1 in eight out of nine tumours that consistently involved the same haplotype on chromosome 9. This haplotype contained a germinal splice site mutation in PTCH1 (NM_001083605:exon9:c.763-6C>A). Analysis of germline DNA confirmed segregation of this mutation with the disease. All BCCs harboured additional somatic loss-of-function (LoF) mutations in the remaining PTCH1 allele which are not typically seen in other cases of NBCCS. This suggests a hypomorphic nature of the germinal PTCH1 mutation in this family. Furthermore, all BCCs had a similar tumour mutational burden compared to BCCs of unrelated NBCCS patients while harbouring a higher number of damaging PTCH1 mutations. Our data suggest that a sequence of three genetic hits leads to the late development of BCCs in two brothers with NBCCS: a hypomorphic germline mutation, followed by somatic LOH and additional mutations that complete PTCH1 inactivation. These genetic events are in line with the late occurrence of the first BCC and with the higher number of damaging PTCH1 mutations compared to usual cases of NBCCS