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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators

We present the second part of a systematic calculation of the two-loop anomalous dimensions for the low-energy effective field theory below the electroweak scale (LEFT): the baryon-number-violating sector at dimension six in the power counting. We obtain the results in two different schemes: in the algebraically consistent ’t Hooft-Veltman scheme for γ 5 , corrected for evanescent as well as chiral-symmetry-breaking effects through finite renormalizations; and in naive dimensional regularization, which in the considered sector of the theory does not lead to any ill-defined γ 5 -odd traces. Our results are of interest for a reanalysis of the constraints on physics beyond the Standard Model from proton-decay searches within an EFT framework at next-to-leading-logarithmic accuracy.

Baryon/Lepton Number Violation↗
DOE OSTI2019

Interplay between Approximation Theory and Renormalization Group

The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory in powers of these parameters, and even when small parameters exist, the related perturbative series are strongly divergent. Second, such perturbative series in powers of these parameters are rather short, so that the standard resummation techniques either yield bad approximations or are not applicable at all. The emphasis in the review is on the methods advanced and developed by the author. One of the general methods is Optimized Perturbation Theory now widely employed in various branches of physics, chemistry, and applied mathematics. The other powerful method is Self-Similar Approximation Theory allowing for quite simple and accurate summation of divergent series. These theories share many common features with the method of renormalization group, which is briefly sketched in order to stress the similarities in their ideas and their mutual interconnection.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1994

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Yakhot, A.↗
DOE OSTI2026

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this paper, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Chemical calculations↗
DOE OSTI2016

Magnetic properties and pairing tendencies of the iron-based superconducting ladder BaFe 2 S 3 : Combined ab initio and density matrix renormalization group study

The recent discovery of superconductivity under high pressure in the two-leg ladder compound BaFe 2 S 3 [H. Takahashi et al., Nat. Mater. 14, 1008 (2015)] opens a broad avenue of research, because it represents the first report of pairing tendencies in a quasi-one-dimensional iron-based high-critical-temperature superconductor. Similarly, as in the case of the cuprates, ladders and chains can be far more accurately studied using many-body techniques and model Hamiltonians than their layered counterparts, particularly if several orbitals are active. In this publication, we derive a two-orbital Hubbard model from first principles that describes individual ladders of BaFe 2 S 3 . The model is studied with the density matrix renormalization group. These first reported results are exciting for two reasons: (i) at half-filling, ferromagnetic order emerges as the dominant magnetic pattern along the rungs of the ladder, and antiferromagnetic order along the legs, in excellent agreement with neutron experiments; and (ii) with hole doping, pairs form in the strong coupling regime, as found by studying the binding energy of two holes doped on the half-filled system. In addition, orbital selective Mott phase characteristics develop with doping, with only oneWannier orbital receiving the hole carriers while the other remains half-filled. Lastly, these results suggest that the analysis of models for iron-based two-leg ladders could clarify the origin of pairing tendencies and other exotic properties of iron-based high-critical-temperature superconductors in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Physics implications of the diphoton excess from the perspective of renormalization group flow

A very plausible explanation for the recently observed diphoton excess at the 13 TeV LHC is a (pseudo)scalar with mass around 750 GeV, which couples to a gluon pair and to a photon pair through loops involving vector-like quarks (VLQs). To accommodate the observed rate, the required Yukawa couplings tend to be large. A large Yukawa coupling would rapidly run up with the scale and quickly reach the perturbativity bound, indicating that new physics, possibly with a strong dynamics origin, is near by. The case becomes stronger especially if the ATLAS observation of a large width persists. In this paper we study the implication on the scale of new physics from the 750 GeV diphoton excess using the method of renormalization group running with careful treatment of different contributions and perturbativity criterion. Our results suggest that the scale of new physics is generically not much larger than the TeV scale, in particular if the width of the hinted (pseudo)scalar is large. Introducing multiple copies of VLQs, lowing the VLQ masses and enlarging VLQ electric charges help reduce the required Yukawa couplings and can push the cutoff scale to higher values. Nevertheless, if the width of the 750 GeV resonance turns out to be larger than about 1 GeV, it is very hard to increase the cutoff scale beyond a few TeVs. This is a strong hint that new particles in addition to the 750 GeV resonance and the vector-like quarks should be around the TeV scale.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Density matrix renormalization group description of the island of inversion isotopes F 28 – 33

Recent experiments have confirmed that the neutron-rich isotopes 28,29 F belong to the so-called island of inversion (IOI), a region of the nuclear chart around Z = 10 and N = 20 where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes 28–33 F are basically unknown. In this study, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes 25–33 F, from a core of 24 O and using an effective two-body interaction with a small number of adjustable parameters in the central and tensor channels. We develop two models adjusted on experimentally confirmed states in 25,26 O and 25–27 F based on different assumptions concerning the positions of the neutron 0d 3/2 and 1p 3/2 shells, and solve the many-body problem using the density matrix renormalization group (DMRG) method for open quantum systems in an sd–fp model space. We obtain the first detailed spectroscopy of 25–33F in the continuum and show how the interplay between continuum effects and deformation explains the recent data on 28,29 F. Several deformed one- and two-neutron halo states are predicted in 29,31 F, and we provide some information about the possible structure of the heaviest fluorine isotopes. We also suggest several experimental studies of interest to constraint models and test the present predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Renormalization group properties of scalar field theories using gradient flow

Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both analytically and on the lattice, distinct from the usual blocking techniques in spin models and gauge theories. In this work, we discuss such a formulation for scalar field theory, and we present preliminary numerical results for its application to the determination of critical exponents at the Wilson-Fisher fixed point of three-dimensional $\phi$4 theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Variational Approach to Monte Carlo Renormalization Group

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. Here, the two-dimensional Ising model is used to illustrate the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Constructing Hubbard models for the hydrogen chain using sliced-basis density matrix renormalization group

Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms and to construct low-energy effective Hubbard-like models. The downfolding procedure first involves a change of basis to a set of atom-centered Wannier functions constructed from the natural orbitals of the exact DMRG one-particle density matrix. The Wannier function model is then reduced to a fewer-parameter Hubbard-like model, whose parameters are determined by minimizing the expectation value of the Wannier Hamiltonian in the ground state of the Hubbard Hamiltonian. This indirect variational procedure not only yields compact and simple models for the hydrogen chain, but also allows us to explore the importance of constraints in the effective Hamiltonian, such as the restricting the range of the single-particle hopping and two-particle interactions, and to assess the reliability of more conventional downfolding. The entanglement entropy for a model's ground state, cut in the middle, is an important property determining the ability of DMRG and tensor networks to simulate the model, and here we study its variation with the range of the interactions. Counterintuitively, we find that shorter ranged interactions often have larger entanglement.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Real Space Renormalization Group Investigation of the Mixed Spins S = 1/2 and S = 3/2 Model

Using a real-space renormalization approach, namely the Migdal-Kadanoff one, we study the mixed Ising system with spins S = 1/2 and S = 3/2 on d-dimensional hypercubic lattice. We have determined the phase diagram in the plane (Δ/|J|, 1/|J|) as well as the eigenvalues of the transformation of the group in the vicinity of the critical points. A comparison with the results of other techniques was carried out.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

On the renormalization group perspective of α-attractors

In this short paper we outline a recipe for the reconstruction of F ( R ) gravity starting from single field inflationary potentials in the Einstein frame. For simple potentials one can compute the explicit form of F ( R ), whilst for more involved examples one gets a parametric form of F ( R ). The F ( R ) reconstruction algorithm is used to study various examples: power-law φ {sup n} , exponential and α -attractors. In each case it is seen that for large R (corresponding to large value of inflaton field), F ( R ) ∼ R {sup 2}. For the case of α -attractors F ( R ) ∼ R {sup 2} for all values of inflaton field (for all values of R ) as α → 0. For generic inflaton potential V (φ), it is seen that if V {sup '}/ V →0 (for some φ) then the corresponding F ( R ) ∼ R {sup 2}. We then study α-attractors in more detail using non-perturbative renormalisation group methods to analyse the reconstructed F ( R ). It is seen that α →0 is an ultraviolet stable fixed point of the renormalisation group trajectories.

79 ASTRONOMY AND ASTROPHYSICS↗