Using a non-perturbative functional renormalization group approach we calculate the renormalized quasi-particle velocity v(k) and the static dielectric function (k) of suspended graphene as functions of an external momentum k. Our numerical result for v(k) can be fitted by v(k)/vF = A+B ln(Λ0/k), where vF is the bare Fermi velocity, Λ0 is an ultraviolet cutoff, and A = 1.37, B = 0.51 for the physically relevant value (e 2 /vF = 2.2) of the coupling constant. In contrast to calculations based on the static random-phase approximation, we find that (k) approaches unity for k → 0. Our result for v(k) agrees very well with a recent measurement by Elias et al. [Nat. Phys. 7, 701 (2011)].PACS numbers: 81.05.ue, 11.10.Hi, At low energies the physical properties of graphene are dominated by the Dirac points where the energy dispersion vanishes linearly. In this regime many-body effects become important and can be measured experimentally [1]. In view of the great interest in graphene both for fundamental research and applied physics, it is important to gain a thorough understanding of correlation effects. Of particular interest is the renormalization of the Fermi velocity at the Dirac points by long-range Coulomb interactions, which has been observed experimentally in suspended graphene using cyclotron resonance [2], in ARPES measurements of quasi-freestanding graphene on SiC [3], and in graphene on hexagonal boron nitride (hBN) [4]. Early one-loop renormalization group (RG) calculations [5] predicted a logarithmic enhancement of the renormalized Fermi velocity,where Λ is the infrared cutoff introduced in the RG procedure, Λ 0 is an ultraviolet cutoff of the order of the inverse lattice spacing, v F = 10 6 m/s is the bare Fermi velocity, and α = e 2 /v F is the relevant dimensionless coupling constant. Because for graphene suspended in vacuum α ≈ 2.2 is rather large, perturbative RG calculations are not expected to be quantitatively accurate.In this work, we use a functional renormalization group (FRG) approach [6,7] to derive non-perturbative RG flow equations for the cutoff-and momentum-dependent velocity v Λ (k) and the static dielectric function Λ (q) of suspended graphene. Since we are interested in the RG flow of momentum-dependent functions, the field theoretical RG is not sufficient, because with this method one can only keep track of a finite set of coupling constants. We show here that this problem can be solved within the FRG formalism [6,7]; specifically, we derive two coupled integro-differential equations for the cutoff-dependent functions v Λ (k) and Λ (q) which are non-perturbative in α and self-consistently describe the interplay between self-energy and screening effects.Our starting point is the following effective Hamiltonian describing the low-energy physics of graphene,where p = ± labels the two Dirac points of the underlying tight-binding model on a honeycomb lattice, v p = pv F is the bare Fermi velocity at Dirac point p, andψ p (k) are two-component fermionic field operators whose components are as...
We present numerically exact results from sign-problem free quantum Monte Carlo simulations for a spinfermion model near an O(3) symmetric antiferromagnetic (AFM) quantum critical point. We find a hierarchy of energy scales that emerges near the quantum critical point. At high energy scales, there is a broad regime characterized by Landau-damped order parameter dynamics with dynamical critical exponent z = 2, while the fermionic excitations remain coherent. The quantum critical magnetic fluctuations are well described by Hertz-Millis theory, except for a T −2 divergence of the static AFM susceptibility. This regime persists down to a lower energy scale, where the fermions become overdamped and concomitantly, a transition into a d−wave superconducting state occurs. These findings resemble earlier results for a spin-fermion model with easy-plane AFM fluctuations of an O(2) SDW order parameter, despite noticeable differences in the perturbative structure of the two theories. In the O(3) case, perturbative corrections to the spin-fermion vertex are expected to dominate at an additional energy scale, below which the z = 2 behavior breaks down, leading to a novel z = 1 fixed point with emergent local nesting at the hot spots [Schlief et al., PRX 7, 021010 (2017)]. Motivated by this prediction, we also consider a variant of the model where the hot spots are nearly locally nested. Within the available temperature range in our study (T ≥ E F 200), we find substantial deviations from the z = 2 Hertz-Millis behavior, but no evidence for the predicted z = 1 criticality. arXiv:2001.00586v3 [cond-mat.str-el]
Z)-w-Trimethylsilyl-(w-2)-alken-1-ols are readily accessible by consecutive superbase metalation and silylation of (w-1)-alken-1-ols. These versatile intermediates may be oxidized to give the corresponding (Z)-w-trimethylsilyl-(w-2)-alkenals which, in the presence of trifluoroacetic acid, can be converted into 2-vinylcycloalkanols such as 2-vinylcyclohexanol (2), isopulegol (4), and bis(2vinylcyclobutyl) ether ( 8). The stereochemical outcome of these cyclization reactions suggests the interference of a novel electrodynamic effect.
Mycoplasma hominis is a commensal of the genitourinary tract, which is infrequently associated with urogenital infections. Extra-urogenital infections due to M. hominis are rare. Here, we report an unusual case of M. hominis subdural empyema in a woman occurring shortly after delivery. The patient presented with symptoms suggestive of bacterial meningitis. Spinal imaging revealed a subdural empyema that required neurosurgical intervention. Cultures from intraoperatively obtained biopsies identified M. hominis as the causative pathogen. The patient was treated with oral moxifloxacin for 4 weeks resulting in the resolution of the spinal lesion. The subdural empyema was presumably caused by a contaminated epidural blood patch performed with the patient's own blood during an episode of transient M. hominis bacteremia after delivery. The blood patch was indicated for the treatment of cerebrospinal fluid leakage, which had occurred after epidural anesthesia. Our findings highlight the significance of transient M. hominis bacteremia after delivery and implicate that M. hominis should be considered as a causative agent of extra-genitourinary tract infections particularly during the postpartum period or after genitourinary manipulation.
We assess numerical stabilization methods employed in fermion many-body quantum Monte Carlo simulations. In particular, we empirically compare various matrix decomposition and inversion schemes to gain control over numerical instabilities arising in the computation of equal-time and time-displaced Green's functions within the determinant quantum Monte Carlo (DQMC) framework. Based on this comparison, we identify a procedure based on pivoted QR decompositions which is both efficient and accurate to machine precision. The Julia programming language is used for the assessment and implementations of all discussed algorithms are provided in the open-source software library StableDQMC.jl.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.