Renormalization group study of interacting electrons

The renormalization-group (RG) approach proposed earlier by Shankar for interacting spinless fermions at $T=0$ is extended to the case of non-zero temperature and spin. We study a model with $SU(N)$-invariant short-range effective interaction and rotationally invariant Fermi surface in two and three dimensions. We show that the Landau interaction function of the Fermi liquid, constructed from the bare parameters of the low-energy effective action, is RG invariant. On the other hand, the physical forward scattering vertex is found as a stable fixed point of the RG flow. We demonstrate that in $d=2$ and 3, the RG approach to this model is equivalent to Landau's mean-field treatment of the Fermi liquid. We discuss subtleties associated with the symmetry properties of the scattering amplitude, the Landau function and the low-energy effective action. Applying the RG to response functions, we find the compressibility and the spin susceptibility as fixed points.Comment: 11 pages, RevTeX 3.0, 2 PostScript figure

Hamiltonian Theory of the Composite Fermion Wigner Crystal

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $\nu=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table

The Fermi Liquid as a Renormalization Group Fixed Point: the Role of Interference in the Landau Channel

We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action's interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zero-angle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid.Comment: 25 pages, RevTeX 3.

Role of Umklapp Processes in Conductivity of Doped Two-Leg Ladders

Recent conductivity measurements performed on the hole-doped two-leg ladder material $\mathrm{Sr_{14-x}Ca_xCu_{24}O_{41}}$ reveal an approximately linear power law regime in the c-axis DC resistivity as a function of temperature for $x=11$. In this work, we employ a bosonic model to argue that umklapp processes are responsible for this feature and for the high spectral weight in the optical conductivity which occurs beyond the finite frequency Drude-like peak. Including quenched disorder in our model allows us to reproduce experimental conductivity and resistivity curves over a wide range of energies. We also point out the differences between the effect of umklapp processes in a single chain and in the two-leg ladder.Comment: 10 pages, 2 figure

Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state

A theory for a Fermi-liquid-like state in a system of charged bosons at filling factor one is developed, working in the lowest Landau level. The approach is based on a representation of the problem as fermions with a system of constraints, introduced by Pasquier and Haldane (unpublished). This makes the system a gauge theory with gauge algebra W_infty. The low-energy theory is analyzed based on Hartree-Fock and a corresponding conserving approximation. This is shown to be equivalent to introducing a gauge field, which at long wavelengths gives an infinite-coupling U(1) gauge theory, without a Chern-Simons term. The system is compressible, and the Fermi-liquid properties are similar, but not identical, to those in the previous U(1) Chern-Simons fermion theory. The fermions in the theory are effectively neutral but carry a dipole moment. The density-density response, longitudinal conductivity, and the current density are considered explicitly.Comment: 32 pages, revtex multicol

Mechanical Properties and Microstructural Characterization of Aged Nickel-based Alloy 625 Weld Metal

The aim of this work was to evaluate the different phases formed during solidification and after thermal aging of the as-welded 625 nickel-based alloy, as well as the influence of microstructural changes on the mechanical properties. The experiments addressed aging temperatures of 650 and 950 A degrees C for 10, 100, and 200 hours. The samples were analyzed by electron microscopy, microanalysis, and X-ray diffraction in order to identify the secondary phases. Mechanical tests such as hardness, microhardness, and Charpy-V impact test were performed. Nondestructive ultrasonic inspection was also conducted to correlate the acquired signals with mechanical and microstructural properties. The results show that the alloy under study experienced microstructural changes when aged at 650 A degrees C. The aging was responsible by the dissolution of the Laves phase formed during the solidification and the appearance of gamma aEuro(3) phase within interdendritic region and fine carbides along the solidification grain boundaries. However, when it was aged at 950 A degrees C, the Laves phase was continuously dissolved and the excess Nb caused the precipitation of the delta-phase (Ni3Nb), which was intensified at 10 hours of aging, with subsequent dissolution for longer periods such as 200 hours. Even when subjected to significant microstructural changes, the mechanical properties, especially toughness, were not sensitive to the dissolution and/or precipitation of the secondary phases

Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

Para-infectious brain injury in COVID-19 persists at follow-up despite attenuated cytokine and autoantibody responses

To understand neurological complications of COVID-19 better both acutely and for recovery, we measured markers of brain injury, inflammatory mediators, and autoantibodies in 203 hospitalised participants; 111 with acute sera (1–11 days post-admission) and 92 convalescent sera (56 with COVID-19-associated neurological diagnoses). Here we show that compared to 60 uninfected controls, tTau, GFAP, NfL, and UCH-L1 are increased with COVID-19 infection at acute timepoints and NfL and GFAP are significantly higher in participants with neurological complications. Inflammatory mediators (IL-6, IL-12p40, HGF, M-CSF, CCL2, and IL-1RA) are associated with both altered consciousness and markers of brain injury. Autoantibodies are more common in COVID-19 than controls and some (including against MYL7, UCH-L1, and GRIN3B) are more frequent with altered consciousness. Additionally, convalescent participants with neurological complications show elevated GFAP and NfL, unrelated to attenuated systemic inflammatory mediators and to autoantibody responses. Overall, neurological complications of COVID-19 are associated with evidence of neuroglial injury in both acute and late disease and these correlate with dysregulated innate and adaptive immune responses acutely