Combining the in-medium similarity renormalization group with the density matrix renormalization group: Shell structure and information entropy
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Astronomy & Astrophysics↗
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Nonlinear Reynolds stress models and the renormalization group
The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.
Rubinstein, Robert↗
Understanding parton evolution in matter from renormalization group analysis
We perform a renormalization group (RG) analysis of collinear hadron production in deep inelastic scattering on nuclei. We consider the limit where the parent parton energy E is large, while the medium opacity remains small. We identify the fixed order and leading enhanced medium contributions to the semi-inclusive cross sections and derive RG equations that resum multiple emissions near the endpoints of the splitting functions at first order in opacity. These evolution equations treat the same type of radiation enhancement in matter as the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi approach, but differ in the way one regulates the collinear divergences. They provide a unique analytic insight into the problem of resummation and a faster and more efficient path to phenomenology. The new RG evolution framework is applied to study fragmentation in eA reactions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Renormalization Group (RG) in Turbulence: Historical and Comparative Perspective
The term renormalization and renormalization group are explained by reference to various physical systems. The extension of renormalization group to turbulence is then discussed; first as a comprehensive review and second concentrating on the technical details of a few selected approaches. We conclude with a discussion of the relevance and application of renormalization group to turbulence modelling.
Zhou, Ye↗
Resurgence of the renormalization group equation
We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.
97 MATHEMATICS AND COMPUTING↗
Continuous-time Monte Carlo renormalization group
We implement the Monte Carlo renormalization group approach in the continuous-time Monte Carlo simulation of a quantum system. In this work, we demonstrate numerically the emergent isotropy between space and time at large distances for the systems that exhibit Lorentz invariance at quantum criticality. Here, this allows us to estimate accurately the sound velocity for these quantum systems. $\textit{Q}$-state Potts models in one and two space dimensions are used to illustrate the method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Development of Renormalization Group Analysis of Turbulence
The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.
L M Smith↗
Renormalization group improvement of the effective potential: an EFT approach
We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
S U ( 2 ) principal chiral model with tensor renormalization group on a cubic lattice
We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean S U ( 2 ) principal chiral field model with the triad tensor renormalization group and the anisotropic tensor renormalization group methods. Using these methods, we find results that are consistent with previous Monte Carlo estimates and the predicted renormalization group scaling of the magnetization close to criticality. These results bring us one step closer to studying finite-density quantum chromodynamics in four dimensions using tensor network methods. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Nonequilibrium renormalization group fixed points of the quantum clock chain and the quantum Potts chain
In this work, we derive an exact renormalization group recursion relation for the Loschmidt amplitude of the quantum Q-state clock model and the quantum Q-state Potts model in one dimension. The renormalization group flow is discussed in detail. The fixed points of the renormalization group flow are found to be complex in general. These fixed points control the dynamical phases of the two models, giving rise to nonanalyticities in its Loschmidt rate function, for both the pure and the disordered system. For the quench protocols studied, dynamical quantum phase transitions are found to occur in the clock model for all Qs considered, while in the Potts model, they only occur when Q < 4 .
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
On ambiguities and divergences in perturbative renormalization group functions
There is an ambiguity in choosing field-strength renormalization factors in the $ \overline{\mathrm{MS}} $ scheme starting from the 3-loop order in perturbation theory. More concerning, trivially choosing Hermitian factors has been shown to produce divergent renormalization group functions, which are commonly understood to be finite quantities. We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry. It turns out that any such divergences can be removed using the renormalization ambiguity and that the use of the flavor-improved β-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa β-functions and provide the first calculation of the flavor-improved 3-loop SM β-functions in the gaugeless limit.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Soviet influences on Kenneth Wilson’s renormalization group work
Here, Kenneth Wilson worked on the renormalization group during the Cold War, when communication between scientists in the Soviet Union and in the West was restricted.Nevertheless, Soviet physicists had a strong influence on Wilson’s work.
99 GENERAL AND MISCELLANEOUS↗
Computational schemes for the Magnus expansion of the in-medium similarity renormalization group
The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schrödinger equation through a continuous unitary transformation of the many-body Hamiltonian. The IMSRG transformation is typically truncated at the normal-ordered two-body level, the IMSRG(2), but recently several approaches have been developed to capture the effects of normal-ordered three-body operators, the IMSRG(3). In particular, a factorized approximation to the IMSRG(3) proposes to capture the leading effects of three-body operators at the same computational cost as the IMSRG(2) approximation. This approach often employs an approximate scheme for solving the IMSRG equations, the so-called hunter-gatherer scheme. In this work, I study the uncertainty associated with this scheme. I find that the hunter-gatherer scheme differs by up to 7MeV for ground-state energies and 0.5MeV for excitation energies from standard IMSRG(2) approaches. These differences are in some cases comparable to the expected size of IMSRG(3) corrections.
39 ≤ A ≤ 58↗
Renormalization group formulation of large eddy simulation
Renormalization group (RNG) methods are applied to eliminate small scales and construct a subgrid scale (SSM) transport eddy model for transition phenomena. The RNG and SSM procedures are shown to provide a more accurate description of viscosity near the wall than does the Smagorinski approach and also generate farfield turbulence viscosity values which agree well with those of previous researchers. The elimination of small scales causes the simultaneous appearance of a random force and eddy viscosity. The RNG method permits taking these into account, along with other phenomena (such as rotation) for large-eddy simulations.
Yakhot, V.↗
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
2-dimensional systems↗
Renormalization group methods for the Reynolds stress transport equations
The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.
Rubinstein, R.↗
Efficient simulation of moiré materials using the density matrix renormalization group
Here we present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction and the large number of orbital degrees of freedom, tBLG is difficult to study with standard DMRG techniques - even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian which we show is both efficient and accurate even when including the spin, valley, and orbital degrees of freedom. To benchmark our approach, we focus mainly on the spinless, single-valley version of the problem where, at half filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moiré materials in future work.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Renormalization-group running of dimension-8 four-fermion operators in the SMEFT
We compute the renormalization-group equations governing the evolution of dimension-8 four-fermion operators in the Standard Model effective field theory (SMEFT). We describe the calculation and present analytic results for both the full flavor structure of the SMEFT and with the assumption of minimal flavor violation. We present numerical results for the renormalization-group evolution of the coefficients, and study their impact on fits of the Large Hadron Collider (LHC) Drell-Yan data. The effects of running on the dimension-8 coefficients can reach 50% or more when evolving from 10 TeV scale down to few-GeV energies relevant for the analysis of fixed-target data. However, the impact of the dimension-8 running on the analysis of Drell-Yan data from the LHC is minimal.
effective field theory↗