Renormalization Group Research Articles

Chern-Simons gravity and PT symmetry

This paper considers the possibility that, starting from a relativistic Hermitian quantum field theory in the ultraviolet (UV) regime, and applying a nonperturbative renormalization-group (RG) flow, we arrive at a situation where there are infrared (IR) singularities in the RG flow of couplings. The latter can be resolved by assuming that the theory can have a phase described by a related non-Hermitian PT-symmetric modification in the IR. The UV-to-IR (Hermitian-to-PT-symmetric) transition can occur in a single renormalization-group flow of the pertinent couplings, as demonstrated in concrete examples. When embedded in a gravitational setting such a transition can lead to a repulsive gravity phase. If there is a RG flow to a repulsive PT -symmetric gravity, then this would be an alternative to dark energy. The discussion here is presented in the context of a string-inspired Chern-Simons gravitational effective action, which involves a pseudoscalar (axionlike) field coupled to Abelian gauge fields and gravity; it may also hold more generally in gravity with torsion. The validity of such a scenario in realistic theories might alleviate the need for de Sitter phases in the current epoch of cosmological evolution, thus avoiding their associated conceptual and technical complications. Published by the American Physical Society 2024

Carboxylesterase 1-Based Drug-Drug Interaction Potential of Remimazolam: In-Vitro Studies and Literature Review.

The ultra-short-acting benzodiazepine remimazolam, approved for procedural sedation and general anesthesia, is inactivated by carboxylesterase 1 (CES1). Remimazolam´s involvement in CES1-mediated drug-drug interactions (DDIs) was investigated. Possible interactions of remimazolam were studied in co-exposure experiments with eleven different drugs. Further, substrates and inhibitors of CES1, identified in the literature, were evaluated for possible in-vivo inhibition using pharmacokinetic and Ki or IC50 values. Compounds with only one published inhibitory concentration and CES1 substrates lacking inhibition data were assigned conservative Ki values. In human liver homogenates and/or blood cells, remimazolam showed no significant inhibition of esmolol and landiolol metabolism, which, in turn, at up to 98 and 169 μM, respectively, did not inhibit remimazolam hydrolysis by human liver homogenates. In human liver S9 fractions, IC50 values ranged from 0.69 μM (simvastatin) and 57 μM (diltiazem) to > 100 μM (atorvastatin) and, for the remaining test items (bupropion, carvedilol, nelfinavir, nitrendipine, and telmisartan), they ranged from 126 to 658 μM. Remifentanil was ineffective even at 1250 μM. Guidance-conforming evaluation revealed no relevant drug-drug interactions with remimazolam via CES1. The algorithm-based predictions were consistent with human study data. Among CES1 inhibitors and substrates identified in the literature, only dapsone and rufinamide were found to be possible in-vivo inhibitors of remimazolam metabolism. Data and analyses suggest a very low potential of remimazolam for pharmacokinetic DDIs mediated by CES1. The theoretical approach and compiled data are not specific to remimazolam and, hence, applicable in the evaluation of other CES1 substrates.

Leading order track functions in a hot and dense QGP

We study the modifications to the fragmentation pattern of partons into charged particles in the presence of a hot and dense quark gluon plasma. To this end, we analyze the perturbative renormalization group equations of the track functions, which describe the energy fraction carried by charged hadrons. Focusing on pure Yang-Mills theory, we compute the lowest-order moments of the medium-modified track functions, which are found to be sensitive to the reduced phase space for emissions in the medium and to energy loss. We use the extracted moments to calculate the energy energy correlator (EEC) on tracks in the collinear limit. The EEC on medium-evolved tracks does not differ qualitatively from the EEC on vacuum tracks despite being sensitive to the color decoherence transition and suppressing the distribution due to quenching, as seen in other jet observables. Published by the American Physical Society 2024

Phase diagram of generalized XY model using the tensor renormalization group

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, T, and the deformation parameter, Δ, and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet. Published by the American Physical Society 2024

Radiative Corrections and the Renormalization Group for the Two-Nucleon Interaction in Effective Field Theory

We use a combination of effective field theory and the renormalization group to determine the impact of radiative corrections on the nucleon–nucleon potential and the binding energy of the deuteron. In order to do so, we present a modified version of pionless effective field theory inspired by earlier work in nonrelativistic quantum electrodynamics. The renormalization group improvement of the deuteron binding energy leads to a shift on the order of a few percent and is consistent with the experimental value. This work serves as a starting point for a dedicated study of radiative corrections in few-body systems relevant for precision tests of the Standard Model in an effective field theory framework.

Optimization of crossover SRK equation of state for thermodynamic properties calculation of CO2

In recent years, the CO2 super/transcritical power cycle has gained significant attention as the most widely studied power cycle. The accurate thermodynamic properties data is very important for cycle design and performance analysis. In this study, the Kiselev's crossover method based on the renormalization group theory is used to improve the classic SRK equation of state in non-critical region and reproduce the critical fluctuation phenomenon in critical region. The nonlinear equations method and interior-point method are used in the parameter fitting of crossover SRK (CSRK) to get the optimal parameters. The replaced method avoids the problem that Newton iteration method is prone to divergence and falling into local optima. The thermodynamic properties of CO2 including the VLE properties, heat capacity and speed of sound are calculated by CSRK, respectively. The results show the calculation of the non-critical region is improved, and the critical fluctuation phenomenon in the near-critical region is described accurately, especially the second-order thermodynamic properties calculation results is improved from 3.65 % to 2.80 % compared with our previous work.

Renormalization-group improved resummation of super-leading logarithms

A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows for the consistent inclusion of the scale dependence of the strong coupling, thereby providing more reliable estimates of the scale uncertainties in theoretical predictions. The key idea is to rearrange the relevant RG evolution operator in such a way that all double-logarithmic corrections are exponentiated from the outset. This forms the starting point for the first resummation of super-leading logarithms at leading order in RG-improved perturbation theory for arbitrary 2 → M scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

Non-Hermitian lattice fermions in the 2D Gross-Neveu-Yukawa model

We work the lattice fermions and non-Hermitian formulation in the 2D Gross-Neveu-Yukawa (GNY) model and demonstrate the numerical implementation for two flavors by the hybrid Monte Carlo. Our approach has a notable advantage in dealing with chiral symmetry on a lattice by avoiding the Nielsen-Ninomiya theorem, due to the nonsymmetrized finite-difference operator. We restore the hypercubic symmetry by averaging over all possible orientations with the proper continuum limit. Our study is the first simulation for the interacting fermion formulated in a non-Hermitian way. We compare the numerical solution with the one-loop resummation. The resummation results matches with the numerical solution in ⟨ϕ⟩, ⟨ϕ2⟩, ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)/2⟩, and ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)ϕ/2⟩. We also used the one-loop resummation to provide the renormalization group flow and asymptotic safety in the 2D GNY model. Published by the American Physical Society 2024

Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces

Abstract We consider the composition of operators with non-closed range in Hilbert spaces and how the nature of ill-posedness is affected by their composition. Specifically, we study the Hausdorff-, Cesàro-, integration operator, and their adjoints, as well as some combinations of those. For the composition of the Hausdorff- and the Cesàro-operator, we give estimates of the decay of the corresponding singular values. As a curiosity, this provides also an example of two practically relevant non-compact operators, for which their composition is compact. Furthermore, we characterize those operators for which a composition with a non-compact operator gives a compact one.

Fractal evolution characteristics of fracture meso-damage in uniaxial compression rock masses using bonded block model

With regard to deep mining in metal mines, an investigation into the failure mode of deep fractured rock masses and their corresponding acoustic emission signal characteristics is conducted via uniaxial compression tests. Subsequently, a fractal damage renormalization group mechanical model is developed to explain the behavior of those fractured rock masses. Employing the bonded block model (BBM) numerical simulation method, fracture process in synthetic rock samples is analyzed, thereby validating the efficacy of the mechanical model. The numerical simulations highlight the critical role of fractures expansion in underlying the deterioration of rock mass strength. As the peak load decreases, the fracture fractal dimension increases, leading to a significant 14.2% reduction in compressive strength accompanied by an approximate 8.7% rise in average fracture fractal dimension. A comparative analysis of tetrahedral and voronoi block synthetic rock samples reveals the tetrahedral block samples exhibit a superior ability to depict the fracture behavior of fractured rock masses. Specifically, they offer a more accurate simulation of acoustic emission characteristics and failure modes. Furthermore, variations in the fracture fractal dimension with respect to the hole defect’s position are observed, with the maximum value occurring along the vertical axis of the hole defect. This observation underscores the potential utility of visually monitoring deep rock fracture dynamics as an effective mean for quantitatively evaluating fracture damage and strength degradation in deep rock formations.

On the interplay between boundary conditions and the Lorentzian Wetterich equation

In the framework of the functional renormalization group and of the perturbative, algebraic approach to quantum field theory (pAQFT), in D’Angelo et al. [Ann. Henri Poinc. 25 (2024) 2295–2352] it has been derived a Lorentzian version of a flow equation à la Wetterich, which can be used to study nonlinear, quantum scalar field theories on a globally hyperbolic spacetime. In this work, we show that the realm of validity of this result can be extended to study interacting scalar field theories on globally hyperbolic manifolds with a timelike boundary. By considering the specific examples of half-Minkowski spacetime and of the Poincaré patch of Anti-de Sitter, we show that the form of the Lorentzian Wetterich equation is strongly dependent on the boundary conditions assigned to the underlying field theory. In addition, using a numerical approach, we are able to provide strong evidences that there is a qualitative and not only a quantitative difference in the associated flow and we highlight this feature by considering Dirichlet and Neumann boundary conditions on half-Minkowski spacetime.

Laplacian renormalization group: an introduction to heterogeneous coarse-graining

The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification into a relatively small set of universality classes. The RG is the most powerful tool for investigating organizational scales within dynamic systems. However, the application of RG techniques to complex networks has presented significant challenges, primarily due to the intricate interplay of correlations on multiple scales. Existing approaches have relied on hypotheses involving hidden geometries and based on embedding complex networks into hidden metric spaces. Here, we present a practical overview of the recently introduced Laplacian RG (LRG) for heterogeneous networks. First, we present a brief overview that justifies the use of the Laplacian as a natural extension of well-known field theories to analyze spatial disorder. We then draw an analogy to traditional real-space RG procedures, explaining how the LRG generalizes the concept of ‘Kadanoff supernodes’ as block nodes that span multiple scales. These supernodes help mitigate the effects of cross-scale correlations due to small-world properties. Additionally, we rigorously define the LRG procedure in momentum space in the spirit of the Wilson RG. Finally, we show different analyses for the evolution of network properties along the LRG flow following structural changes when the network is properly reduced.

Light-ray sum rules and the c-anomaly

In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly ∆a has been related to the average null energy. We extend this result to derive a sum rule for the other anomaly coefficient, ∆c, in terms of the stress tensor three-point function. While the sum rule for ∆a is an expectation value of the averaged null energy operator, and therefore positive, the result for ∆c involves the off-diagonal matrix elements, so it does not have a fixed sign.

A functional renormalization group for signal detection and stochastic ergodicity breaking

Signal detection is one of the main challenges in data science. As often happens in data analysis, the signal in the data may be corrupted by noise. There is a wide range of techniques that aim to extract the relevant degrees of freedom from data. However, some problems remain difficult. This is notably the case for signal detection in almost continuous spectra when the signal-to-noise ratio is small enough. This paper follows a recent bibliographic line, which tackles this issue with field-theoretical methods. Previous analysis focused on equilibrium Boltzmann distributions for an effective field representing the degrees of freedom of data. It was possible to establish a relation between signal detection and Z2 -symmetry breaking. In this paper, we consider a stochastic field framework inspired by the so-called ‘model A’, and show that the ability to reach, or not reach, an equilibrium state is correlated with the shape of the dataset. In particular, by studying the renormalization group of the model, we show that the weak ergodicity prescription is always broken for signals that are small enough, when the data distribution is close to the Marchenko–Pastur law. This, in particular, enables the definition of a detection threshold in the regime where the signal-to-noise ratio is small enough.

Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice

We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricted partition functions. We benchmark our method with Metropolis Monte Carlo simulations. The analysis of fixed points reveals information of location of the Fisher zeros and we provide a conjecture about the location of zeros in terms of the boundary of the basins of attraction.

CTMRG study of the critical behavior of an interacting-dimer model

The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically using the corner transfer matrix renormalization group algorithm. The critical exponents are known to depend on the chemical potential of vacancies, or monomers. At large average density of the latter, the phase transition becomes the first-order. We compute the scaling dimensions of both the order parameter and temperature in the second-order regime and compare them with the conjecture that the critical behavior is the same as the Ashkin–Teller model on its self-dual critical line.

Quasi-critical dynamics in large-scale social systems regulated by sudden events.

How do heterogeneous individual behaviors arise in response to sudden events and how do they shape large-scale social dynamics? Based on a five-year naturalistic observation of individual purchasing behaviors, we extract the long-term consumption dynamics of diverse commodities from approximately 2.2 million purchase orders. We subdivide the consumption dynamics into trend, seasonal, and random components and analyze them using a renormalization group. We discover that the coronavirus pandemic, a sudden event acting on the social system, regulates the scaling and criticality of consumption dynamics. On a large time scale, the long-term dynamics of the system, regardless of arising from trend, seasonal, or random individual behaviors, is pushed toward a quasi-critical region between independent (i.e., the consumption behaviors of different commodities are irrelevant) and correlated (i.e., the consumption behaviors of different commodities are interrelated) phases as the pandemic erupts. On a small time scale, short-term consumption dynamics exhibits more diverse responses to the pandemic. While the trend and random behaviors of individuals are driven to quasi-criticality and exhibit scale-invariance as the pandemic breaks out, seasonal behaviors are more robust against regulations. Overall, these discoveries provide insights into how quasi-critical macroscopic dynamics emerges in heterogeneous social systems to enhance system reactivity to sudden events while there may exist specific system components maintaining robustness as a reflection of system stability.

The renormalization group for large-scale structure: primordial non-Gaussianities

The renormalization group for large-scale structure (RG-LSS) describes the evolution of galaxy bias and stochastic parameters as a function of the cutoff Λ. In this work, we introduce interaction vertices that describe primordial non-Gaussianity into the Wilson-Polchinski framework, thereby extending the free theory to the interacting case.The presence of these interactions forces us to include new operators and bias coefficients to the bias expansion to ensure closure under renormalization.We recover the previously-derived “scale-dependent bias” contributions, as well as a new (subdominant) stochastic contribution.We derive the renormalization group equations governing the RG-LSS for a large class of interactions which account for vertices at linear order in f NL that parametrize interacting scalar and massive spinning fields during inflation.Solving the RG equations, we show the evolution of the non-Gaussian contributions to galaxy clustering as a function of scale.

Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder

We document the ground state phase diagram of the one-dimensional Kitaev chain with quasi-periodic disorder in the presence of two-body interactions. Our data were obtained for systems of L=1000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L=1000$$\\end{document} sites using large-scale density-matrix renormalization group numerics and is benchmarked against known results for the clean system. We demonstrate that moderate quasi-periodic disorder stabilizes the topological phase both for repulsive and attractive interactions. For larger disorder strengths, the system features re-entrance behavior and multiple phase transitions.Graphical abstractPhase diagram as a function of the chemical potential and the disorder strength for repulsive interactions

Equilibrium atmospheric boundary layer model for numerical simulation of urban wind environment

The numerical simulation of urban wind environments faces difficulties in capturing the turbulent characteristics due to the large computational domain. Traditional Reynolds-averaged methods (RANS) can effectively capture the average wind characteristics of urban areas. However, due to the significant dissipation and attenuation of turbulent energy in the downstream direction, this method fails to provide accurate turbulent characteristics after time-averaging processing. Therefore, in order to obtain a higher-precision turbulent wind field distribution within urban areas, this paper proposed a new numerical method named an equilibrium atmospheric boundary layer model (EABL) by modifying the control equation of the shear stress transport k–ω model. During the process, the equilibrium atmospheric boundary layer was achieved successfully, and the attenuation problem of the turbulent kinetic energy and dissipation rate during the computational fluid dynamics numerical simulation was resolved. Simultaneously, a wind tunnel experiment and six turbulence models [standard k–ε, realizable k–ε, renormalization group k–ε, large eddy simulation—narrowband synthesis random flow generator (LES-NSRFG) and LES vortex method and EABL] were employed to simulate the wind field characteristics in an actual residential area. The simulation results demonstrate that, relative to traditional RANS models, the EABL model enhances the simulation accuracy of turbulence characteristics by over two times. Furthermore, compared to LES models, the EABL model can reduce computational time by threefold.