Renormalization Analysis Research Articles

Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals

We establish and develop a novel methodology to treat higher-order non-linear effects of gravitational radiation that is scattered from binary inspirals, which employs modern scattering-amplitudes methods on the effective picture of the binary as a composite particle. We spell out our procedure to study such effects: assembling tree amplitudes via generalized-unitarity methods and employing the closed-time-path formalism to derive the causal effective actions, which encompass the full conservative and dissipative dynamics. We push through to a new state of the art for these higher-order effects, up to the third subleading tail effect, at order GN5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {G}_N^5 $$\\end{document} and the 5-loop level, which corresponds to the 8.5PN order. We formulate the consequent dissipated energy for these higher-order corrections, and carry out a renormalization analysis, where we uncover new subleading RG flow of the quadrupole coupling. For all higher-order tail effects we find perfect agreement with partial observable results in PN and self-force theories, where available.

Renormalization Analysis of Magnetohydrodynamics: Two-Loop Approximation

Renormalization Analysis of Magnetohydrodynamics: Two-Loop Approximation

Where is the Quantum Spin Nematic?

We provide strong evidence of the spin-nematic state in a paradigmatic ferro-antiferromagnetic J_{1}-J_{2} model using analytical and density-matrix renormalization group methods. In zero field, the attraction of spin-flip pairs leads to a first-order transition and no nematic state, while pair repulsion at larger J_{2} stabilizes the nematic phase in a narrow region near the pair-condensation field. A devil's staircase of multipair condensates is conjectured for weak pair attraction. A suppression of the spin-flip gap by many-body effects leads to an order-of-magnitude contraction of the nematic phase compared to naïve expectations. The proposed phase diagram should be broadly valid.

Hub-collision avoidance and leaf-node options algorithm for fractal dimension and renormalization of complex networks.

The box-covering method plays a fundamental role in the fractal property recognition and renormalization analysis of complex networks. This study proposes the hub-collision avoidance and leaf-node options (HALO) algorithm. In the box sampling process, a forward sampling rule (for avoiding hub collisions) and a reverse sampling rule (for preferentially selecting leaf nodes) are determined for bidirectional network traversal to reduce the randomness of sampling. In the box selection process, the larger necessary boxes are preferentially selected to join the solution by continuously removing small boxes. The compact-box-burning (CBB) algorithm, the maximum-excluded-mass-burning (MEMB) algorithm, the overlapping-box-covering (OBCA) algorithm, and the algorithm for combining small-box-removal strategy and maximum box sampling with a sampling density of 30 (SM30) are compared with HALO in experiments. Results on nine real networks show that HALO achieves the highest performance score and obtains 11.40%, 7.67%, 2.18%, and 8.19% fewer boxes than the compared algorithms, respectively. The algorithm determinism is significantly improved. The fractal dimensions estimated by covering four standard networks are more accurate. Moreover, different from MEMB or OBCA, HALO is not affected by the tightness of the hubs and exhibits a stable performance in different networks. Finally, the time complexities of HALO and the compared algorithms are all O(N2), which is reasonable and acceptable.

Analytical renormalization group approach to competing orders at charge neutrality in twisted bilayer graphene

We investigate twisted bilayer graphene near charge neutrality using a generalized Bistritzer-MacDonald continuum model accounting for corrugation effects. The Fermi velocity vanishes for particular twist angles properly reproducing the physics of the celebrated magic angles. Using group representation theory, we identify all contact interaction potentials compatible with the symmetries of the model. This enables us to identify two classes of quartic interactions leading to either the opening of a gap or to nematic ordering. We then implement a renormalization group analysis to study the effect of quantum fluctuations on the appearance of these states for twist angles approaching the first magic value. This combined group theory-renormalization study reveals that the proximity to the first magic angle favors the occurrence of a layer-polarized, gapped state with a spatial modulation of interlayer correlations, which we call a nematic insulator.

Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions.

Dissipative quantum phase transition has been widely believed to occur in a Josephson junction coupled to a resistor despite a lack of concrete experimental evidence. Here, on the basis of both numerical and analytical nonperturbative renormalization group analyses, we reveal breakdown of previous perturbative arguments and defy the common wisdom that the transition always occurs at the quantum resistance R_{Q}=h/(4e^{2}). We find that renormalization group flows in nonperturbative regimes induce nonmonotonic renormalization of the charging energy and lead to a qualitatively different phase diagram, where the insulator phase is strongly suppressed to the deep charge regime (Cooper pair box), while the system is always superconducting in the transmon regime. We identify a previously overlooked dangerously irrelevant term as an origin of the failure of conventional understandings. Our predictions can be tested in recent experiments realizing high-impedance long superconducting waveguides and would provide a solution to the long-standing controversy about the fate of dissipative quantum phase transition in the resistively shunted Josephson junction.

Effects of a single impurity in a Luttinger liquid with spin–orbit coupling

In quasi-1D conducting nanowires spin–orbit coupling destructs spin–charge separation, intrinsic to Tomonaga–Luttinger liquid (TLL). We study renormalization of a single scattering impurity in a such liquid. Performing bosonization of low-energy excitations and exploiting perturbative renormalization analysis we extend the phase portrait in K σ − K ρ space, obtained previously for TLL with decoupled spin–charge channels.

Proton decay matrix elements on the lattice at physical pion mass

Proton decay is a major prediction of grand-unified theories (GUT) and its observation would indicate baryon number violation that is required for baryogenesis. Many decades of searching for proton decay have constrained its rate and ruled out some of the simplest GUT models. Apart from the baryon number-violating interactions, this rate also depends on transition amplitudes between the protons and mesons or leptons produced in the decay, which are matrix elements of three-quark operators. We report the nonperturbative calculation of these matrix elements for the most studied two-body decay channels into a meson and antilepton done on a lattice with physical light and strange quark masses and lattice spacings $a\ensuremath{\approx}0.14\text{ }\text{ }\mathrm{fm}$ and 0.20 fm. We perform nonperturbative renormalization and excited state analysis to control associated systematic effects. Our results largely agree with previous lattice calculations done with heavier quark masses and thus remove ambiguity in ruling out some simple GUT theories due to quark mass dependence of hadron structure.

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work we solve the low-energy physics using an unbiased numerically exact tensor network method named the "rigorous renormalization group." We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree-Fock-type treatment of the $z$ couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally-correlated XY spin chain with arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.

Self-dualities and renormalization dependence of the phase diagram in 3d O(N) vector models

In the classically unbroken phase, 3d O(N) symmetric ϕ4 vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by κ) and for any N. It is shown that for κ = κ∗ the two fixed points merge and then, for κ < κ∗, they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the N = 1 ϕ4 theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d O(N) models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large N in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase.

Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups

Our goal in this paper is to present a generalization of the spectral zeta regularization for general Feynman amplitudes on Riemannian manifolds. Our method uses complex powers of elliptic operators but involves several complex parameters in the spirit of analytic renormalization by Speer, to build mathematical foundations for the renormalization of perturbative interacting quantum field theories. Our main result shows that spectrally regularized Feynman amplitudes admit analytic continuation as meromorphic germs with linear poles in the sense of the works of Guo–Paycha and the second author. We also give an explicit determination of the affine hyperplanes supporting the poles. Our proof relies on suitable resolution of singularities of products of heat kernels to make them smooth. As an application of the analytic continuation result, we use a universal projection from meromorphic germs with linear poles on holomorphic germs to construct renormalization maps which subtract singularities of Feynman amplitudes of Euclidean fields. Our renormalization maps are shown to satisfy consistency conditions previously introduced in the work of Nikolov–Todorov–Stora in the case of flat space-times.

Euclidean black saddles and AdS4 black holes

We find new asymptotically locally AdS4 Euclidean supersymmetric solutions of the STU model in four-dimensional gauged supergravity. These “black saddles” have an S1× {Sigma}_{mathfrak{g}} boundary at asymptotic infinity and cap off smoothly in the interior. The solutions can be uplifted to eleven dimensions and are holographically dual to the topologically twisted ABJM theory on S1× {Sigma}_{mathfrak{g}} . We show explicitly that the on-shell action of the black saddle solutions agrees exactly with the topologically twisted index of the ABJM theory in the planar limit for general values of the magnetic fluxes, flavor fugacities, and real masses. This agreement relies on a careful holographic renormalization analysis combined with a novel UV/IR holographic relation between supergravity parameters and field theory sources. The Euclidean black saddle solution space contains special points that can be Wick-rotated to regular Lorentzian supergravity backgrounds that correspond to the well-known supersymmetric dyonic AdS4 black holes in the STU model.

Exact and density matrix renormalization group studies of two mixed spin- (12,52,12) branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

The mixed-spin Ising-Heisenberg and Heisenberg branched chains whose magnetic backbone consists of regularly alternating spins 1/2 and 5/2, the latter of which are additionally coupled to an extra spin 1/2 providing lateral branching, are investigated using exact analytical and density matrix renormalization group (DMRG) methods. The proposed spin-chain models capture some relevant aspects of the heterotrimetallic coordination polymer $[\mathrm{Cu}\mathrm{Mn}(\mathrm{L})][\mathrm{Fe}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{Cl}{\mathrm{O}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$. The mixed spin-$(1/2,5/2,1/2)$ Ising-Heisenberg branched chain is exactly solvable under the assumption of an Ising-like exchange coupling along the chain, while the lateral branching is treated as an anisotropic $XXZ$ Heisenberg exchange interaction. We determine the ground-state phase diagram and quantify a bipartite quantum entanglement between dimers at lateral branching. It is shown that the studied mixed-spin Ising-Heisenberg branched chain accurately fits available experimental data for temperature dependence of the magnetic susceptibility. The ground-state phase diagram of the analogous mixed spin-$(1/2,5/2,1/2)$ Heisenberg branched chain is obtained within the DMRG method. The ground-state phase diagrams of the Ising-Heisenberg and its full Heisenberg counterpart are contrasted. In particular, the ground-state phase diagram of the mixed-spin Heisenberg branched chain involves a special Gaussian critical point, for which a proper finite-size scaling analysis is provided to accurately estimate its location and the correlation length critical exponent.

Interacting Rice-Mele model: Bulk and boundaries

We investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we firstly compute the single-particle spectral function, the local density, and the boundary charge in the absence of interactions. The boundary charge is fully determined by bulk properties indicating a bulk-boundary correspondence. In a large parameter regime it agrees with the one obtained from an effective low-energy theory (arXiv:2004.00463). Secondly, we investigate the robustness of our results towards two-particle interactions. To resum the series of leading logarithms for small gaps, which dismantle plain perturbation theory in the interaction, we use an essentially analytical renormalization group approach. It is controlled for small interactions and can directly be applied to the microscopic lattice model. We benchmark the results against numerical density matrix renormalization group data. The main interaction effect in the bulk is a power-law renormalization of the gap with an interaction dependent exponent. The important characteristics of the boundary charge are unaltered and can be understood from the renormalized bulk properties, elevating the bulk-boundary correspondence to the interacting regime. This requires a consistent treatment not only of the low-energy gap renormalization but also of the high-energy band width one. In contrast to low-energy field theories our renormalization group approach also provides the latter. We show that the interaction spoils the relation between the bulk properties and the number of edge states, consistent with the observation that the Rice-Mele model with finite potential modulation does not reveal any zero-energy edge states.

Interacting Dirac materials

We investigate the extent to which the class of Dirac materials in two-dimensions provides general statements about the behavior of both fermionic and bosonic Dirac quasiparticles in the interacting regime. For both quasiparticle types, we find common features for the interaction induced renormalization of the conical Dirac spectrum. We perform the perturbative renormalization analysis and compute the self-energy for both quasiparticle types with different interactions and collate previous results from the literature whenever necessary. Guided by the systematic presentation of our results in table , we conclude that long-range interactions generically lead to an increase of the slope of the single-particle Dirac cone, whereas short-range interactions lead to a decrease. The quasiparticle statistics does not qualitatively impact the self-energy correction for long-range repulsion but does affect the behavior of short-range coupled systems, giving rise to different thermal power-law contributions. The possibility of a universal description of the Dirac materials based on these features is also mentioned.

Anomalous diffusion of acoustic waves in 2D periodic media: Radiative transport and renormalization analysis.

This work investigates the occurrence of anomalous transport of acoustic waves propagating in two-dimensional (2D) perfectly periodic media and presents dedicated analysis tools to explore and understand the properties of the medium controlling the transitions between different transport regimes. By leveraging a two-fold approach that combines both radiative transport and renormalization theory, the propagation properties of the inhomogeneous medium can be characterized both near and at the transition from normal to anomalous diffusion. The proposed approach builds upon the classical radiative transfer theory of bulk materials, and it is specifically designed to study 2D systems. The ability to simulate and interpret the field quantities that describe such transport mechanisms can play a significant role in the development of wave-based imaging technology for highly inhomogeneous and scattering media.

Solving the speed and accuracy of box-covering problem in complex networks

The box-covering method that covers a network with a minimum number of boxes is critical to demonstrate network fractals and the re-normalization analysis of complex networks. Moreover, one is able to investigate the network structure by analyzing the re-normalization flow or categorizing networks into several universal classes. A number of compelling methods are not well adapted to the large-scale networks due to high time complexity, or low accuracy. In this paper, we introduce a hybrid method that has high accuracy and low time consumption based the maximum-excluded-mass-burning (MEMB) method and the random sequential (RS) method. Our method combines the characteristics of the MEMB method that search as fewer boxes as possible with the high efficiency of the RS method by selecting a few unimportant central nodes, especially for large-scale networks. We also optimize the storage mechanism of the method so that the excluded mass of nodes can be updated efficiently. Experiments in the real networks with different structures demonstrate that the improvement of our method can be substantial. Our method reduces the time consumption of the MEMB method by more than 40% with only 10% more boxes than the MEMB method.

Renormalizable enhanced tensor field theory: The quartic melonic case

Tensor field theory is the quantum field theoretic counterpart of tensor models and enhanced tensor field theory enlarges this theory space to accommodate “enhanced tensor interactions.” These interactions were introduced to explore new large N limits and to probe different phases for tensor models. We undertake the multi-scale renormalization analysis for two types of enhanced theories with rank d tensor fields ϕ:(U(1)D)d→C and with the so-called quartic “melonic” interactions of the form p2aϕ4 reminiscent of derivative couplings expressed in momentum space. Scrutinizing the degree of divergence of both theories, we identify generic conditions for their renormalizability at all orders of perturbation at high momenta, i.e., the ultraviolet regime. For the first type of theory, we identify a 2-parameter space of just-renormalizable models for generic (d, D). These models have dominant non-melonic four-point functions. Finally, by specifying the parameters, we detail the renormalization analysis of the second type of model which is more exotic: it exhibits an infinite family of logarithmically divergent two-point amplitudes and all four-point amplitudes are convergent.

Renormalization analysis for degenerate ground states

We consider a Hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons. We show that the ground state projection and the ground state energy are analytic functions of the coupling constant in a cone with apex at the origin, provided a mild infrared assumption holds. To show the result operator theoretic renormalization is used and extended to degenerate situations.

Improved wall boundary conditions in the incompressible smoothed particle hydrodynamics method

PurposeThe purpose of this paper is to improve the 2D incompressible smoothed particle hydrodynamics (ISPH) method by working on the wall boundary conditions in ISPH method. Here, two different wall boundary conditions in ISPH method including dummy wall particles and analytical kernel renormalization wall boundary conditions have been discussed in details.Design/methodology/approachThe ISPH algorithm based on the projection method with a divergence velocity condition with improved boundary conditions has been adapted.FindingsThe authors tested the current ISPH method with the improved boundary conditions by a lid-driven cavity for different Reynolds number 100 ≤ Re ≤ 1,000. The results are well validated with the benchmark problems.Originality/valueIn the case of dummy wall boundary particles, the homogeneous Newman boundary condition was applied in solving the linear systems of pressure Poisson equation. In the case of renormalization wall boundary conditions, the authors analytically computed the renormalization factor and its gradient based on a quintic kernel function.