Symmetry-based Model Research Articles

Naturalness-motivated composite Higgs model for generating the top Yukawa coupling

The large top Yukawa coupling results in the top quark contributing significantly to the quantum correction of the Higgs mass term. Traditionally, this effect is canceled by the presence of top partners in symmetry-based models. However, the absence of light top partners poses a challenge to the naturalness of these models. In this paper, we study a model based on composite Higgs with the top Yukawa coupling originating from dimension-six four-fermion operators. The low cutoff scale of the top quark loop required by the naturalness principle can be realized with a light gauge boson Eμ that connects the hyperfermions and top quarks. A scalarless dynamical model with weakly coupled extended SU(4)EC gauge group is presented. The model features an Eμ boson and a ZE′ boson both at the sub-TeV scale, which lead to a rich phenomenology, especially in the top quark physics. Published by the American Physical Society 2024

Variation from closed-shell to open shell electronic structures in oligothiophene bis(dioxolene) complexes.

A series of oligothiophene bis(dioxolene) complexes, SQ-Thn-SQ (SQ = S = ½TpCum,MeZnII(3-tert-butyl-orthosemiquinonate); TpCum,Me = tris(5-cumenyl-3-methylpyrazolyl)borate anion) have been synthesized, structurally characterized, and studied as a function of the number of thiophene bridging units, n (n = 0-3) using a combination of variable-temperature (VT) electronic absorption and EPR spectroscopies, and VT magnetic susceptibility measurements. The thiophene bridge bond lengths determined by X-ray crystallography display dramatic differences across the SQ-Thn-SQ series. Bridge bond deviation values (Σ|Δi|) display a progressive change in the nature of the bridge fragment bonding as the number of thiophene groups increases, with quinoidal bridge character for n = 1 (SQ-Th-SQ) and biradical character with "aromatic" bridge bond lengths for n = 3 (SQ-Th3-SQ). Remarkably, for n = 2 (SQ-Th2-SQ) the nature of the bridge fragment is intermediate between quinoid and biradical aromatic, which we describe as having open-shell character as opposed to biradicaloid since the open-shell biradical configuration does not have the correct symmetry to mix with the quinoidal ground-state configuration. This bridge bonding character is reflected in the energies of the lowest lying open-shell states for these three molecules. The SQ-Th-SQ molecule is diamagnetic at all temperatures studied, and we provide evidence for SQ-SQ antiferromagnetic exchange coupling and population of triplet states in SQ-Th2-SQ and SQ-Th3-SQ, with JSQ-SQ(ave) = -279 cm-1 (VT EPR/electronic absorption/magnetic susceptibility) and JSQ-SQ = -117 cm-1 (VT EPR/electronic absorption/magnetic susceptibility), respectively. The results have been interpreted in the context of state configurational mixing within a simplified 4-electron, 3-orbital model that explicitly contains contributions of a bridge fragment. Variable-temperature spectroscopic- and magnetic susceptibility data are consistent with two low-lying open-shell states for SQ-Th3-SQ, but three low-lying states (one closed-shell and two open-shell) for SQ-Th2-SQ. This model provides a simple symmetry-based framework to understand the continuum of electronic and geometric structures of this class of molecules as a function of the number of thiophene units in the bridge.

Quantifying Social Interventions for Combating COVID-19 via a Symmetry-Based Model.

The COVID-19 pandemic has revealed new features in terms of substantial changes in rates of infection, cure, and death as a result of social interventions, which significantly challenges traditional SEIR-type models. In this paper we developed a symmetry-based model for quantifying social interventions for combating COVID-19. We found that three key order parameters, separating degree (S) for susceptible populations, healing degree (H) for mild cases, and rescuing degree (R) for severe cases, all display logistic dynamics, establishing a novel dynamic model named SHR. Furthermore, we discovered two evolutionary patterns of healing degree with a universal power law in 23 areas in the first wave. Remarkably, the model yielded a quantitative evaluation of the dynamic back-to-zero policy in the third wave in Beijing using 12 datasets of different sizes. In conclusion, the SHR model constitutes a rational basis by which we can understand this complex epidemic and policymakers can carry out sustainable anti-epidemic measures to minimize its impact.

Proximity effects in graphene on monolayers of transition-metal phosphorus trichalcogenides MPX3 (M:Mn, Fe, Ni, Co, and X: S, Se)

We investigate the electronic band structure of graphene on a series of two-dimensional magnetic transition-metal phosphorus trichalcogenide monolayers, ${M\text{P}X}_{3}$ with $M={\mathrm{Mn},\mathrm{Fe},\mathrm{Ni},\mathrm{Co}}$ and $X={\mathrm{S},\mathrm{Se}}$, with first-principles calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and sublattice resolved proximity-induced exchange couplings (${\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}$ and ${\ensuremath{\lambda}}_{\text{ex}}^{\text{B}}$) from the low-energy Dirac bands of the proximitized graphene. Depending on the magnetic phase of the ${M\text{P}X}_{3}$ layer (ferromagnetic and three antiferromagnetic ones), completely different Dirac dispersions can be realized with exchange splittings ranging from 0 to 10 meV. Remarkably, not only the magnitude of the exchange couplings depends on the magnetic phase, but also the global sign and the type. Important, one can realize uniform $({\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}\ensuremath{\approx}{\ensuremath{\lambda}}_{\text{ex}}^{\text{B}})$ and staggered $({\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}\ensuremath{\approx}\ensuremath{-}{\ensuremath{\lambda}}_{\text{ex}}^{\text{B}})$ exchange couplings in graphene. From selected cases we find that the interlayer distance, as well as a transverse electric field, are efficient tuning knobs for the exchange splittings of the Dirac bands. More specifically, decreasing the interlayer distance by only about 10%, a giant fivefold enhancement of proximity exchange is found, while applying few V/nm of electric field, provides tunability of proximity exchange by tens of percent. We have also studied the dependence on the Hubbard $U$ parameter and find it to be weak. Moreover, we find that the effect of SOC on the proximitized Dirac dispersion is negligible compared to the exchange coupling.

Gegenbauer’s Twin

In Twin Higgs models the dominant source of fine-tuning is the cancellation of order v2/f2 required to obtain a Standard Model-like Higgs, where v and f are the electroweak and new physics scales, respectively. Recently proposed Gegenbauer Goldstone models naturally realise v2/f2 « 1 and hence remove this source of fine-tuning. By combining the two into ‘Gegenbauer’s Twin’, we obtain a symmetry-based model for Higgs-sector naturalness consistent with current collider measurements without fine-tuning of parameters. Single-Higgs coupling deviations of a few percent and trilinear self-coupling deviations of order one are irreducible in the natural parameter space. Thus, notably, the fingerprints of Gegenbauer’s Twin could emerge first through di-Higgs measurements at the High-Luminosity LHC.

Anisotropic magnetic interactions in hexagonalAB-stacked kagome lattice structures: Application toMn3X(X=Ge,Sn,Ga) compounds

${\mathrm{Mn}}_{3}X$ compounds in which the magnetic $\mathrm{Mn}$ atoms form $AB$-stacked kagome lattices have received a tremendous amount of attention since the observation of the anomalous Hall effect in ${\mathrm{Mn}}_{3}\mathrm{Ge}$ and ${\mathrm{Mn}}_{3}\mathrm{Sn}$. Although the magnetic ground state has been known for some time to be an inverse triangular structure with an induced in-plane magnetic moment, there have been several controversies about the minimal magnetic Hamiltonian. We present a general symmetry-based model for these compounds that includes a previously unreported interplane Dzyaloshinskii-Moriya interaction, as well as anisotropic exchange interactions. The latter are shown to compete with the single-ion anisotropy which strongly affects the ground state configurations and elementary spin-wave excitations. Finally, we present the calculated elastic and inelastic neutron scattering intensities and point to experimental assessment of the types of magnetic anisotropy in these compounds that may be important.

Graphene on two-dimensional hexagonal BN, AlN, and GaN: Electronic, spin-orbit, and spin relaxation properties

We investigate the electronic structure of graphene on a series of 2D hexagonal nitride insulators hXN, X = B, Al, and Ga, with DFT calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and spin-orbit coupling (SOC) from the low-energy Dirac bands of proximitized graphene. While commensurate hBN induces a staggered potential of about 10 meV into the Dirac bands, less lattice-matched hAlN and hGaN disrupt the Dirac point much less, giving a staggered gap below 100 $\mu$eV. Proximitized intrinsic SOC surprisingly does not increase much above the pristine graphene value of 12 $\mu$eV; it stays in the window of (1-16) $\mu$eV, depending strongly on stacking. However, Rashba SOC increases sharply when increasing the atomic number of the boron group, with calculated maximal values of 8, 15, and 65 $\mu$eV for B, Al, and Ga-based nitrides, respectively. The individual Rashba couplings also depend strongly on stacking, vanishing in symmetrically-sandwiched structures, and can be tuned by a transverse electric field. The extracted spin-orbit parameters were used as input for spin transport simulations based on Chebyshev expansion of the time-evolution of the spin expectation values, yielding interesting predictions for the electron spin relaxation. Spin lifetime magnitudes and anisotropies depend strongly on the specific (hXN)/graphene/hXN system, and they can be efficiently tuned by an applied external electric field as well as the carrier density in the graphene layer. A particularly interesting case for experiments is graphene/hGaN, in which the giant Rashba coupling is predicted to induce spin lifetimes of 1-10 ns, short enough to dominate over other mechanisms, and lead to the same spin relaxation anisotropy as observed in conventional semiconductor heterostructures: 50\%, meaning that out-of-plane spins relax twice as fast as in-plane spins.

QM-sym, a symmetrized quantum chemistry database of 135 kilo molecules

Applying deep learning methods in materials science research is an important way of solving the time-consuming problems of typical ab initio quantum chemistry methodology, but due to the size of large molecules, large and uncharted fields still exist. Implementing symmetry information can significantly reduce the calculation complexity of structures, as they can be simplified to the minimum symmetric units. Because there are few quantum chemistry databases that include symmetry information, we constructed a new one, named QM-sym, by designing an algorithm to generate 135k organic molecules with the Cnh symmetry composite. Those generated molecules were optimized to a stable state using Gaussian 09. The geometric, electronic, energetic, and thermodynamic properties of the molecules were calculated, including their orbital degeneracy states and orbital symmetry around the HOMO-LUMO. The basic symmetric units were also included. This database p rovides consistent and comprehensive quantum chemical properties for structures with Cnh symmetries. QM-sym can be used as a benchmark for machine learning models in quantum chemistry or as a dataset for training new symmetry-based models.

Custodial glide symmetry of quantum spin Hall edge modes in monolayer WTe2

A monolayer of WTe$_2$ has been shown to display quantum spin Hall (QSH) edge modes persisting up to 100~K in transport experiments. Based on density-functional theory calculations and symmetry-based model building including the role of correlations and substrate support, we develop an effective electronic model for WTe$_2$ which fundamentally differs from other prototypical QSH settings: we find that the extraordinary robustness of quantum spin Hall edge modes in WTe$_2$ roots in a glide symmetry due to which the topological gap opens away from high-symmetry points in momentum space. While the indirect bulk gap is much smaller, the glide symmetry implies a large direct gap of up to 1~eV in the Brillouin zone region of the dispersing edge modes, and hence enables sharply boundary-localized QSH edge states depending on the specific boundary orientation.

Bifurcation and stability analysis with the role of normal form symmetries on the harmonic streamwise forced oscillation of the cylinder wake

The dynamics of the cylinder wake subjected to harmonic inline oscillation is investigated in this work. Two-dimensional numerical computations are performed for Re=200 to find the effect of inline sinusoidal oscillation on the flow pattern leading to the variation of cylinder lift, drag and wake shedding frequency. Two complex primary modes of the v-velocity field, resulting from a proper orthogonal decomposition (POD) analysis, are considered to model and predict the nonlinear forced wake dynamics governed by the interaction of vortex shedding modes. The equivariant bifurcation theory in the presence of normal form symmetry O(2)×S1 is employed to classify the mode interaction solution branches with respect to lower order symmetries. The coupled amplitude equations are developed with the frequency saturation information included by the addition of complex coefficients. The symmetry-based model is expanded up to 7th power thus including spatio-temporal effects. The coefficients of the model are obtained from CFD simulations. The novelty of this work is that the amplitude equations are derived purely from the mode symmetries and not from a Galerkin reduction of the Navier–Stokes equations.The inline cylinder oscillation effect on the wake dynamics is captured by bifurcation analysis of this model under the variation of the two linear coefficients. As the oscillation amplitude increases, two limit cycles of the model undergo a symmetry-breaking bifurcation leading to a quasi-periodic state. For amplitude-to-diameter ratio A∕D=0.5, the quasi-periodic state undergoes a torus doubling bifurcation. The bifurcated mode S frequency matches the lift coefficient shedding frequency for A∕D=0.5, obtained from the numerical (CFD) computations. The bifurcated modulated traveling waves have mode S as the dominant v-velocity mode, which confirms the symmetric period-doubled quasi-steady v-velocity pattern observed in CFD. The stability behavior of the bifurcated solution branches is also captured in the Poincare plane. The model correctly predicts the bifurcation sequence of the wake dynamic. This knowledge opens the possibility to develop low order controllers for the wake–structure interaction.

Electromagnetic properties in 160-170Dy nuclei: A microscopic description by the pseudo- SU(3) shell model

The large collectivity observed in the rare-earth region of the nuclear landscape is well known. The microscopic studies are difficult to perform in this region due to the enormous size of the valence spaces, a problem that can be avoided by means of the use of symmetry-based models. Here we present calculations for electromagnetic properties of 160-170Dy nuclei within the pseudo-SU(3) scheme. The model Hamiltonian includes the preserving symmetry \( Q\cdot Q\) term and the symmetry-breaking Nilsson and pairing terms, systematically parametrized for all members of the chain. The model is used to calculate B(E2) and B(M1) inter-band transition strengths between the ground state, \( \gamma\) and \( \beta\) -bands. In addition, we present results for quadrupole moments and g factors in these rotational bands. The results show that the pseudo-SU(3) shell model is a powerful microscopic theory for a description of electromagnetic properties of states in the normal parity sector in heavy deformed nuclei.

Center clusters in full QCD at finite temperature and background magnetic field

We study the center structure of full dynamical QCD at finite temperatures and nonzero values of the background magnetic field using continuum extrapolated lattice data. We concentrate on two particular observables characterizing center clusters: their fractality and the probability for percolation. For temperatures below and around the transition region, the fractal dimension is found to be significantly smaller than three, leading to a vanishing mean free path inside the cluster structure. This finding might be relevant for center symmetry-based models of heavy-ion collisions. In addition, the percolation probability is employed to define the transition temperature and to map out the QCD phase diagram in the magnetic field-temperature plane.

Formation of fragment momentum correlations in three-body predissociation of triatomic hydrogen: The interplay of geometry-dependent nonadiabatic coupling and ground-state dynamics

Momentum correlations in three-body predissociation of triatomic hydrogen are investigated by quasiclassical trajectory calculations. It is shown that nonadiabatic couplings that trigger predissociation of the $2{\mathit{sA}}_{1}^{'}$ state of ${\mathrm{H}}_{3}$ imprint their geometric properties on the momentum correlation structures observed after dissociation. A simple symmetry-based model of the geometric coupling properties succeeds in reproducing most of the experimentally observed patterns. The ground-state dynamics that transform the geometric properties of the coupling into the final momentum correlations are identified.

Mechanism of Homotropic Control to Coordinate Hydrolysis in a Hexameric AAA+ Ring ATPase

AAA+ proteins are ubiquitous mechanochemical ATPases that use energy from ATP hydrolysis to remodel their versatile substrates. The AAA+ characteristic hexameric ring assemblies raise important questions about if and how six often identical subunits coordinate hydrolysis and associated motions. The PspF AAA+ domain, PspF1–275, remodels the bacterial σ54–RNA polymerase to activate transcription. Analysis of ATP substrate inhibition kinetics on ATP hydrolysis in hexameric PspF1–275 indicates negative homotropic effects between subunits. Functional determinants required for allosteric control identify: (i) an important link between the ATP bound ribose moiety and the SensorII motif that would allow nucleotide-dependent α-helical α/β subdomain dynamics; and (ii) establishes a novel regulatory role for the SensorII helix in PspF, which may apply to other AAA+ proteins. Consistent with functional data, homotropic control appears to depend on nucleotide state-dependent subdomain angles imposing dynamic symmetry constraints in the AAA+ ring. Homotropic coordination is functionally important to remodel the σ54 promoter. We propose a structural symmetry-based model for homotropic control in the AAA+ characteristic ring architecture.

Identification of Boundaries in Parallel Noun Phrases: A Probabilistic Swapping Model

Parallel structure is a way to factor out common constituents in the expressions, which makes an effect of simplification of expressions. The complexity can be greatly reduced at the phase of sentence parsing by identifying such boundaries of parallel structure.In this paper, we propose a probabilistic model to identify parallel cores (corresponding constituents) as well as boundaries of parallel noun phrases conjoined by "wa/gwa" (conjunctive particle in Korean). It is based on the idea of swapping constituents, utilizing symmetry (two or more identical constituents are repeated) and reversibility (the order of constituents is changeable) in parallel structure. The probabilities are calculated from (unlabelled) corpus with parallel structures, which is an advantage over the approaches trained with labeled corpus. Our model, moreover, is not dependent on languages.It is also shown that the semantic features of the modifiers around parallel noun phrase and the patterns among words can be utilized further to correct the boundaries identified by the swapping model.Experiment shows that our probabilistic swapping model performs much better than symmetry-based model and machine learning based approaches.

Theory and Application of Dissociative Electron Capture in Molecular Identification

The coupling of an electron monochromator (EM) to a mass spectrometer (MS) has created a new analytical technique, EM-MS, for the investigation of electrophilic compounds. This method provides a powerful tool for molecular identification of compounds contained in complex matrices, such as environmental samples. In particular, EM-MS has been applied to the detection of nitrated aromatic compounds, many of which are potent mutagens and/or carcinogens and are considered environmental hazards. EM-MS expands the application and selectivity of traditional MS through the inclusion of a new dimension in the space of molecular characteristics-the electron resonance energy spectrum. EM-MS also enhances detection sensitivity as well because the entire electron flux of the proper energy can be delivered into the negative ion resonance that is analytically most useful to solving the problem at hand. However, before this tool can realize its full potential, it will be necessary to create a library of resonance energy scans from standards of the molecules for which EM-MS offers a practical means of detection. Unfortunately, the number of such standards is very large and not all of the compounds are commercially available, making this library difficult to construct. Here, an approach supplementing direct measurement with chemical inference and quantum scattering theory is presented to demonstrate the feasibility of directly calculating resonance energy spectra. This approach makes use of the symmetry of the transition-matrix element of the captured electron to discriminate between the spectra of isomers. As a way of validating this approach, the resonance values for 25 nitrated aromatic compounds were measured along with their relative abundance. Subsequently, the spectra for the isomers of nitrotoluene were shown to be consistent with the symmetry-based model. The initial success of this treatment suggests that it might be possible to predict negative ion resonances and thus create a library of EM-MS standards.

Article

The role of Lie groups and algebras in symmetry-based models of the genetic code is considered. The two schemes, based upon the symplectic group Sp(6) and the exceptional group G(2) are shown to correspond to different embeddings in the group SO(14). Some possible alternative schemes are sketched. Problems with considering codons being represented as fermionic or bosonic are noted. A complete listing is given of all 64-dimensional irrecducible representations that can arise in the symmetric and alternating groups. PACS Nos.: 87.10 and 02.20

Lattice vibrations in compounds crystallising with the baryte structure

The observation that the baryte structure [Pnma(D162h)] results from a distortion of a structure with lower unit cell occupancy [Imma(D282h)] provides, for compounds crystallising with this lattice, a symmetry-based model for the assignment of the lattice vibrations at k= 0 in which relative band intensities are used as assignment criteria.

Symmetry-based model for the modulated phases of betaine calcium chloride dihydrate.

A symmetry-based model for betaine calcium chloride dihydrate (BCCD) is presented. BCCD is a crystal with many modulated phases that can be commensurate or incommensurate. In our model, BCCD is viewed as formed of layers, perpendicular to which the crystal is modulated. The free energy is expanded in terms of amplitudes of symmetry modes of these layers. Which symmetry modes must appear in the free energy is determined through experimental data on the phonon-dispersion relation. For a previous related work, the phonon-dispersion relation was not yet available and the necessary assumption of which modes should be included proved to be incorrect. In the free energy, competing interactions between the symmetry modes lead to different phases

Erratum: A symmetry-based model for selective rotational energy transfer in collisions of spherical top molecules [J. Chem. Phys. 9 3, 8731 (1990)

Erratum: A symmetry-based model for selective rotational energy transfer in collisions of spherical top molecules [J. Chem. Phys. <b>9</b> <b>3</b>, 8731 (1990)