Fermi Liquids and the Luttinger Integral

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral $I_{\rm L}$, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of $I_{\rm L}$ with $I_{\rm L}=\pm\pi/2$, occur in impurity models in phases with non-analytic low energy scattering, classified as singular Fermi liquids. Here we show the same values, $I_{\rm L}=\pm\pi/2$, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.Comment: 5 pages 7 figure

Renormalized parameters and perturbation theory for an n-channel Anderson model with Hund's rule coupling: Asymmetric case

We explore the predictions of the renormalized perturbation theory for an n-channel Anderson model, both with and without Hund's rule coupling, in the regime away from particle-hole symmetry. For the model with n=2 we deduce the renormalized parameters from numerical renormalization group calculations, and plot them as a function of the occupation at the impurity site, nd. From these we deduce the spin, orbital and charge susceptibilities, Wilson ratios and quasiparticle density of states at T=0, in the different parameter regimes, which gives a comprehensive overview of the low energy behavior of the model. We compare the difference in Kondo behaviors at the points where nd=1 and nd=2. One unexpected feature of the results is the suppression of the charge susceptibility in the strong correlation regime over the occupation number range 1 <nd <3.Comment: 9 pages, 17 figure

Autosomal recessive primary microcephaly: an analysis of locus heterogeneity and phenotypic variation

BACKGROUND AND OBJECTIVES: Locus heterogeneity is well established in autosomal recessive primary microcephaly (MCPH) and to date five loci have been mapped. However, the relative contributions of these loci have not been assessed and genotype-phenotype correlations have not been investigated. DESIGN: A study population of 56 consanguineous families resident in or originating from northern Pakistan was ascertained and assessed by the authors. A panel of microsatellite markers spanning each of the MCPH loci was designed, against which the families were genotyped. RESULTS: The head circumference of the 131 affected subjects ranged from 4 to 14 SD below the mean, but there was little intrafamilial variation among affecteds (± 1 SD). MCPH5 was the most prevalent, with 24/56 families consistent with linkage; 2/56 families were compatible with linkage to MCPH1, 10/56 to MCPH2, 2/56 to MCPH3, none to MCPH4, and 18/56 did not segregate with any of the loci. CONCLUSIONS: MCPH5 is the most common locus in this population. On clinical grounds alone, the phenotype of families linked to each MCPH locus could not be distinguished. We have also shown that further MCPH loci await discovery with a number of families as yet unlinked

Orbitally-driven Behavior: Mott Transition, Quantum Oscillations and Colossal Magnetoresistance in Bilayered Ca3Ru2O7

We report recent transport and thermodynamic experiments over a wide range of temperatures for the Mott-like system Ca3Ru2O7 at high magnetic fields, B, up to 30 T. This work reveals a rich and highly anisotropic phase diagram, where applying B along the a-, b-, and c-axis leads to vastly different behavior. A fully spin-polarized state via a first order metamagnetic transition is obtained for B||a, and colossal magnetoresistance is seen for B||b, and quantum oscillations in the resistivity are observed for B||c, respectively. The interplay of the lattice, orbital and spin degrees of freedom are believed to give rise to this strongly anisotropic behavior.Comment: 26 pages and 8 figure

Kufor-Rakeb syndrome, pallido-pyramidal degeneration with supranuclear upgaze paresis and dementia, maps to 1p36

Kufor-Rakeb syndrome is an autosomal recessive nigro-striatal-pallidal-pyramidal neurodegeneration. The onset is in the teenage years with clinical features of Parkinson’s disease plus spasticity, supranuclear upgaze paresis, and dementia. Brain scans show atrophy of the globus pallidus and pyramids and, later, widespread cerebral atrophy. We report linkage in Kufor- Rakeb syndrome to a 9 cM region of chromosome 1p36 delineated by the markers D1S436 and D1S2843, with a maximum multipoint lod score of 3.6. (J Med Genet 2001;38:680–682

Phase diagram and critical points of a double quantum dot

We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct interaction $U_{12}$ and an exchange interaction $J$. The model has two types of quantum critical points, one at $J=J_c$ to a local singlet state and one at $U_{12}=U_{12}^c$ to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale $T^*$ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at $J=J_c$. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.Comment: 18 pages 31 figure

Convergence of energy scales on the approach to a local quantum critical point

We find the emergence of strong correlations and universality on the approach to the quantum critical points of a two impurity Anderson model. The two impurities are coupled by an inter-impurity exchange interaction $J$ and direct interaction $U_{12}$ and are hybridized with separate conduction channels.The low energy behavior is described in terms of renormalized parameters, which can be deduced from numerical renormalization group (NRG) calculations. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor $z\to 0$, and the renormalized parameters can be expressed in terms of a single energy scale $T^*$. The values of the renormalized interaction parameters in terms of $T^*$ can be predicted from the condition of continuity of the spin and charge susceptibilities, and correspond to strong correlation as they are greater than or equal to the effective band width. These predictions are confirmed by the NRG calculations, including the case when the onsite interaction U=0.Comment: 5 pages 5 figure