Renormalization Of Parameters Research Articles

Density-matrix mean-field theory

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

Elementary examples of renormalization from mechanics and integral calculus

Two classical mechanical systems—block-and-tackle machines and nonlinear oscillators—exhibit renormalization of numerical parameters. A simple one-dimensional integral illustrates several other facets of renormalization (regularization, renormalization group, resummation). These examples provide insight for students and non-specialists into the workings of a subtle, complicated and historically misunderstood subject.

Nonperturbative running of the tensor operator for Nf=3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the nonsinglet tensor operator, for Nf=3 QCD with Wilson fermions in a mixed action setup, with standard Schrödinger functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger functional (χSF) boundary conditions for valence quarks. Based on a recursive finite-size scaling technique we compute nonperturbatively the tensor step-scaling function for an energy range between a hadronic scale and an electroweak scale, above which perturbation theory may be safely applied. Our result is expressed as the RG-running factor TRGI/[T(μhad)]R, where the numerator is the scale independent (renormalization group invariant—RGI) tensor operator and the denominator is its renormalized counterpart at a hadronic scale μhad=233(8) MeV in a given scheme. We determine the step-scaling function in four distinct renormalization schemes. We also compute the renormalization parameters of these schemes at μhad which, combined with the RG-running factor, gives the scheme-independent quantity ZTRGI(g02) in four schemes and for a range of bare gauge couplings in which large volume hadronic matrix element simulations are performed by the CLS consortium in Nf=2+1 QCD. All four results are compatible and also agree with a recent determination based on a unitary setup for Wilson quarks with Schrödinger functional boundary conditions [arXiv:2309.04314]. This provides a strong universality test. Published by the American Physical Society 2024

Theoretical determination of Ising-type transition by using the Self-Consistent Harmonic Approximation

Over the years, the Self-Consistent Harmonic Approximation (SCHA) has been successfully utilized to determine the transition temperature of many different magnetic models, particularly the Berezinskii–Thouless–Kosterlitz transition in two-dimensional ferromagnets. More recently, the SCHA has found application in describing ferromagnetic samples in spintronic experiments. In such a case, the SCHA has proven to be an efficient formalism for representing the coherent state in the ferromagnetic resonance state. One of the main advantages of using the SCHA is the quadratic Hamiltonian, which incorporates thermal spin fluctuations through renormalization parameters, keeping the description simple while providing excellent agreement with experimental data. In this article, we investigate the SCHA application in easy-axis magnetic models, a subject that has not been adequately explored to date. We obtain both semiclassical and quantum approaches of the SCHA for a general anisotropic magnetic model and employ them to determine various quantities such as the transition temperature, spin-wave energy spectrum, magnetization, and critical exponents. To verify the accuracy of the method, we compare the SCHA results with experimental and Monte Carlo simulation data for many distinct well-known magnetic materials.

Leading power accuracy in lattice calculations of parton distributions

In lattice-QCD calculations of parton distribution functions (PDFs) via large-momentum effective theory, the leading power (twist-three) correction appears as O(ΛQCD/Pz) due to the linear-divergent self-energy of Wilson line in quasi-PDF operators. For lattice data with hadron momentum Pz of a few GeV, this correction is dominant in matching, as large as 30% or more. We show how to eliminate this uncertainty through choosing the mass renormalization parameter consistently with the resummation scheme of the infrared-renormalon series in perturbative matching coefficients. An example on the lattice pion PDF data at Pz=1.9 GeV shows an improvement of matching accuracy by a factor of more than 3∼5 in the expansion region x=0.2∼0.5.

Functional-renormalization-group approach to circuit quantum electrodynamics

A nonperturbative approach is developed to analyze superconducting circuits coupled to quantized electromagnetic continuum within the framework of the functional renormalization group. The formalism allows us to determine complete physical pictures of equilibrium properties in the circuit quantum electrodynamics (cQED) architectures with high-impedance waveguides, which have recently become accessible in experiments. We point out that nonperturbative effects can trigger a breakdown of the supposedly effective descriptions, such as the spin-boson and boundary sine-Gordon models, and lead to qualitatively unique phase diagrams. The origin of the failure of conventional understandings is traced to strong renormalizations of circuit parameters at low-energy scales. Our results indicate that a nonperturbative analysis is essential for a comprehensive understanding of cQED platforms consisting of superconducting circuits and long high-impedance transmission lines.

Robustness and sensitivity of some wavelet multifractal models in fractal data modelling

AbstractMany multifractal models such as self‐similar and scaling law types have been proved to be efficient modellers and estimators in many fields such as financial time series where the data hide fractal and multifractal structures, allowing its processing without sophisticated models to be difficult. However, in statistical analysis, a necessary part that should take place for any model and estimator consists in tests of performance such as confidence intervals and generally statistical tests to confirm the adequacy of the model. The present paper provides the consideration of multifractal models based on wavelets and self‐similar type processes to study statistical tests. To test the efficiency, accuracy and robustness of the models, different inferential statistics are introduced, provided with some empirical examples due to the EURO/USD exchange rate time series with a sample covering the period 03/01/2000 to 30/08/2022. Contrarily to existing works, we showed in the present work that quasi‐self‐similar type models are better for many reasons. They indeed guarantee the well fitting of the data dynamics, the nonlinearity in both the model and the multifractal spectrum, the renormalization parameters which may differ from one scale to another and the preservation of the quasi multiplicative structure.

Linear Stability of Semiclassical Theories of Gravity

The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model mimics also the evolution induced by semiclassical Einstein equations, such as the one which describes the early universe in the cosmological case. The equations governing the dynamics of linear perturbations around simple exact solutions of this toy model are analyzed by constructing the corresponding retarded fundamental solutions, and by discussing the corresponding initial value problem. It is shown that, if the quantum field which drives the back-reaction to the classical background is massive, then there are choices of the renormalization parameters for which the linear perturbations with compact spatial support decay polynomially in time for large times, thus indicating stability of the underlying semiclassical solution.

Consistency of potential energy in the dynamical vertex approximation

In the last decades, dynamical mean-field theory (DMFT) and its diagrammatic extensions have been successfully applied to describe local and nonlocal correlation effects in correlated electron systems. Unfortunately, except for the exact solution, it is impossible to fulfill both the Pauli principle and conservation laws at the same time. Consequently, fundamental observables such as the kinetic and potential energies are ambiguously defined. In this work, we propose an approach to overcome the ambiguity in the calculation of the potential energy within the ladder dynamical vertex approximation (D$\Gamma$A) by introducing an effective mass renormalization parameter in both the charge and the spin susceptibility of the system. We then apply our method to the half-filled single-band Hubbard model on a three-dimensional bipartite cubic lattice. We find that: (i) at weak-to-intermediate coupling, a reasonable modification of the transition temperature $\TN$ to the antiferromagnetically ordered state with respect to previous ladder D$\Gamma$A calculations without charge renormalization. This is in good agreement with dual fermion and Monte Carlo results; (ii) the renormalization of charge fluctuations in our new approach leads to a unique value for the potential energy which is substantially lower than corresponding ones from DMFT and non-self-consistent ladder D$\Gamma$A; and (iii) the hierarchy of the kinetic energies between the DMFT and the ladder D$\Gamma$A in the weak coupling regime is restored by the consideration of charge renormalization.

Field Theory of Interacting Boundary Gravitons

Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by GG and \LambdaΛ. As a consequence, correlation functions of the boundary stress tensor in AdS_33 are uniquely fixed in terms of one dimensionless parameter, which is the central charge of the Virasoro algebra. The same argument implies that AdS_33 gravity at a finite radial cutoff is a renormalizable theory, but now with one additional parameter corresponding to the cutoff location. This theory is conjecturally dual to a T\overline{T}TT¯-deformed CFT, assuming that such theories actually exist. To elucidate this, we study the quantum theory of boundary gravitons living on a cutoff planar boundary and the associated correlation functions of the boundary stress tensor. We compute stress tensor correlation functions to two-loop order (GG being the loop counting parameter), extending existing tree level results. This is made feasible by the fact that the boundary graviton action simplifies greatly upon making a judicious field redefinition, turning into the Nambu-Goto action. After imposing Lorentz invariance, the correlators at this order are found to be unambiguous up to a single undetermined renormalization parameter.

Theoretical analysis of FMR-driven spin pumping current and its properties via the self-consistent harmonic approximation

We applied the self-consistent harmonic approximation (SCHA), combined with coherent states formalism, to study the ferromagnetic resonance (FMR) in a ferromagentic/normal metal junction. Due to the interface interaction, the FMR-generated spin current is injected from the magnetic insulator to the normal metal, the so-called spin pumping. Ordinarily, ferromagnetic models are described by bosonic representation or phenomenological theories; however, in a coherent magnetization state, the SCHA is the more natural choice to treat FMR problems. Over the years, the SCHA has successfully applied to investigate ferro- and antiferromagnetism in a wide range of scenarios. The main point of the SCHA formalism involves the adoption of a quadratic model for which corrections are included through temperature-dependent renormalization parameters. Therefore the SCHA is an efficient method for determining the properties of magnetically ordered phases. Using the SCHA, we obtained the temperature dependence of FMR-driven spin pumping. In addition, we found the spin-mix conductance, the additional damping from the angular momentum injection into the normal metal side, and the magnetic susceptibility. The SCHA outcomes are in remarkable agreement with the results of the literature.

Effectiveness of the Self-Consistent Harmonic Approximation in ferromagnets with dipolar interactions

Among the various methods for treating magnetic models, the Self-Consistent Harmonic Approximation (SCHA) has successfully described ferro and antiferromagnetism in many different scenarios. In particular, the SCHA is a valuable and easy formalism for determining transition temperatures as, for example, the Berezinskii–Kosterlitz–Thouless. The heart of the method includes thermal fluctuations through of a renormalization parameter depending on temperature. Nevertheless, most of the work has been done considering only short-range interactions, which results in an incomplete description of actual magnetic samples. Here, we generalize the SCHA to include the dipolar interaction in the thermodynamic analysis. The method is applied to analyze the well-known Europium Chalcogenides EuO and EuS. The SCHA results are in good agreement with the experimental measurements.

Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations. Part I. Standard Model

The renormalization of vacuum expectation value parameters, such as v in the Standard Model (SM), is an important ingredient in electroweak renormalization, where this issue is connected to the treatment of tadpoles. Tadpole counterterms can be generated in two different ways in the Lagrangian: in the course of parameter renormalization, or alternatively via Higgs field redefinitions. The former typically leads to small corrections originating from tadpoles, but in general suffers from gauge dependences if overline{mathrm{MS}} renormalization conditions are used for mass parameters. The latter is free from gauge dependences, but is prone to very large corrections in overline{mathrm{MS}} schemes, jeopardizing perturbative stability in predictions. In this paper we propose a new scheme for tadpole renormalization, dubbed Gauge-Invariant Vacuum expectation value Scheme (GIVS), which is a hybrid scheme of the two mentioned types, with the benefits of being gauge independent and perturbatively stable. The GIVS is based on the gauge-invariance property of Higgs fields, and the corresponding parameters like v, in non-linear representations of Higgs multiplets. We demonstrate the perturbative stability of the GIVS in the SM by discussing the conversion between on-shell and overline{mathrm{MS}} renormalized masses.

Spin-phonon coupling in ferrimagnet spinel CoMn2O4.

Coupling of material properties provides new fundamental insights and possibilities toward multifunctional devices. The spinel structures display strong coupling between different order parameters, as a consequence, exhibiting many fascinating properties, such as multiferroicity and superconductivity. Here, we have investigated the structural, magnetic, and vibrational properties of mixed-spinel CoMn2O4 stabilized in distorted tetragonal structures as evidenced from x-ray diffraction measurements. Magnetization measurements reveal two ferrimagnetic phase transitions at 185 and 90K. Raman scattering measurements reveal the renormalization of phonon parameters for a few phonon modes at low temperatures, arising from spin-phonon coupling. The obtained value for λS2 is ∼2cm-1. The strength of spin-phonon coupling (λ) is estimated according to the spins involved in the corresponding lattice vibrations and discussed.

Nonperturbative running of the quark mass for Nf=3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the quark mass, for ${N}_{f}=3$ QCD with Wilson fermions in a mixed action setup, with standard Schr\"odinger functional (SF) boundary conditions for sea quarks and chirally rotated Schr\"odinger functional ($\ensuremath{\chi}\mathrm{SF}$) boundary conditions for valence quarks. This necessitates the tuning of the boundary factor ${z}_{\mathrm{f}}({g}_{0}^{2})$ of the $\ensuremath{\chi}\mathrm{SF}$ valence action, in order to ensure that QCD symmetries are fully recovered in the continuum. The properties of this novel setup are monitored through the ratios ${Z}_{S}/{Z}_{P}$ and ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ of the renormalization parameters and step scaling functions of the scalar and pseudoscalar densities. Where comparison is possible, our ${Z}_{S}/{Z}_{P}$ results are found to agree with previous determinations, based on a mass ratio method [G. M. de Divitiis et al. (ALPHA Collaboration), Eur. Phys. J. C 79, 797 (2019)] and Ward identities [ J. Heitger et al. (ALPHA Collaboration), Eur. Phys. J. C 80, 765 (2020); J. Heitger et al., Eur. Phys. J. C 81, 606 (2021)], with Schr\"odinger functional boundary conditions. The behavior of ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ confirms the theoretical expectations of $\ensuremath{\chi}\mathrm{SF}$ QCD, related to the restoration of the theory's symmetries in the continuum limit. From the step-scaling function of the pseudoscalar density we obtain the quark mass RG-running function from hadronic to perturbative energy scales. This is fully compatible with the earlier result obtained in a similar setup for Wilson quarks with Schr\"odinger functional boundary conditions [I. Campos et al., Eur. Phys. J. C 78, 387 (2018)], and provides a strong universality test for the two lattice setups.

Confined vortex surface and irreversibility. 2. Hyperbolic sheets and turbulent statistics

We continue the study of Confined Vortex Surfaces (CVS) that we introduced in the previous paper. We classify the solutions of the CVS equation and find the analytical formula for the velocity field for arbitrary background strain eigenvalues in the stable region. The vortex surface cross-section has the form of four symmetric hyperbolic sheets with a simple equation [Formula: see text] in each quadrant of the tube cross-section ([Formula: see text] plane). We use the dilute gas approximation for the vorticity structures in a turbulent flow, assuming their size is much smaller than the mean distance between them. We vindicate this assumption by the scaling laws for the surface shrinking to zero in the extreme turbulent limit. We introduce the Gaussian random background strain for each vortex surface as an accumulation of a large number of small random contributions coming from other surfaces far away. We compute this self-consistent background strain, relating the variance of the strain to the energy dissipation rate. We find a universal asymmetric distribution for energy dissipation. A new phenomenon is a probability distribution of the shape of the profile of the vortex tube in the [Formula: see text] plane. This phenomenon naturally leads to the “multifractal” scaling of the moments of velocity difference [Formula: see text]. More precisely, these moments have a nontrivial dependence of [Formula: see text], [Formula: see text], approximating power laws with effective index [Formula: see text]. We derive some general formulas for the moments containing multidimensional integrals. The rough estimate of resulting moments shows the log–log derivative [Formula: see text] which is approximately linear in [Formula: see text] and slowly depends on [Formula: see text]. However, the value of effective index is wrong, which leads us to conclude that some other solution of the CVS equations must be found. We argue that the approximate phenomenological relations for these moments suggested in a recent paper by Sreenivasan and Yakhot are consistent with the CVS theory. We reinterpret their renormalization parameter [Formula: see text] in the Bernoulli law [Formula: see text] as a probability to find no vortex surface at a random point in space.

Effectiveness of the Self-Consistent Harmonic Approximation in Ferromagnets with Dipolar Interactions

Among the various methods for treating magnetic models, the Self-Consistent Harmonic Approximation (SCHA) has successfully described ferro and antiferromagnetism in many different scenarios. In particular, the SCHA is a valuable and easy formalism for determining transition temperatures as, for example, the Berezinskii-Kosterlitz-Thouless. The heart of the method includes thermal fluctuations through of a renormalization parameter depending on temperature. Nevertheless, most of the work has been done considering only short-range interactions, which results in an incomplete description of actual magnetic samples. Here, we generalize the SCHA to include the dipolar interaction in the thermodynamic analysis. The method is applied to analyze the well-known Europium Chalcogenides EuO and EuS. The SCHA results are in good agreement with the experimental measurements.

Two-loop application of the Breitenlohner-Maison/\u2019t Hooft-Veltman scheme with non-anticommuting \u03b35: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

We apply the BMHV scheme for non-anticommuting γ5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.

A thermophysically balanced multiscale coarse-grained potential for glass-forming polymers with the energy renormalization method

Coarse-grained molecular dynamics simulations are a widely accepted methodology in the field of studying the viscoelasticity of elastomers. In this paper, a thermophysically balanced multiscale coarse-grained potential for glass-forming polymers is presented with the energy renormalization (ER) method by redefining temperature transferable correlation effects between rescaling factors for energy parameter and length-scale parameter. The correlation effects have not been investigated in the literature, to the best knowledge of authors. The coarse-grained potential was demonstrated for the polyisoprene model generated from the anionic polymerization. The ER enables temperature transferability by adopting renormalization parameters as function of the temperature. Considering the correlation effects, a multi objective-optimization algorithm was adopted to find proper solution sets of and matching mean square displacement (MSD) and density to the all-atom model simultaneously. Meanwhile, shear stress was matched to find first, then, density was fitted in the low-temperature regime. To verify the coarse-grained potential in the middle-temperature regime, MSD was compared to those from the all-atom model, and it was successfully matched.

A Graph Convolutional Network With Multiple Dependency Representations for Relation Extraction

Dependency analysis can assist neural networks to capture semantic features within a sentence for entity relation extraction (RE). Both hard and soft strategies of encoding dependency tree structure have been developed to balance the beneficial extra information against the unfavorable interference in the task of RE. A wide application of graph convolutional network (GCN) in the field of natural language processing (NLP) has demonstrated its effectiveness in encoding the input sentence with the dependency tree structure, as well as its efficiency in parallel computation. This study proposes a novel GCN-based model using multiple representations to depict the dependency tree from various perspectives, and combines those dependency representations afterward to obtain a better sentence representation for relation classification. This model can maximally draw from the sentence the semantic features relevant to the relationship between entities. Results show that our model achieves state-of-the-art performance in terms of the F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> score (68.0) on the Text Analysis Conference relation extraction dataset (TACRED). In addition, we verify that the renormalization parameter in the GCN operation should be carefully chosen to help GCN-based models achieve its best performance.