Mechanism Of Spontaneous Symmetry Breaking Research Articles

Steven Weinberg and Higgs physics

As a tribute to Steven Weinberg, we summarize the immense impact that he had on the understanding of the mechanism of spontaneous symmetry breaking and on the physics of the Higgs boson. In particular, four landmark contributions to this field are highlighted. A first one is his early work with Goldstone and Salam on spontaneously broken continuous symmetries that paved the way to the Higgs mechanism. A second towering breakthrough is his model of leptons which later became the Standard Model of particle physics and for which he was awarded the Nobel prize with Glashow and Salam. A third seminal work is the so-called Weinberg-Linde lower bound on the Higgs boson mass that was derived from the requirement of the stability of the electroweak vacuum. Finally, we summarize his important contributions in model-building of new physics with extended Higgs sectors and their possible impact in flavor physics and CP-violation. The historical aspects as well as the contemporary way of viewing these four major topics are summarized and their impact on today Higgs physics, and more generally particle physics, is highlighted.

Ricci reheating reloaded

A Hubble-induced phase transition is a natural spontaneous symmetry breaking mechanism allowing for explosive particle production in non-oscillatory models of inflation involving non-minimally coupled spectator fields. In this work, we perform a comprehensive characterisation of this type of transitions as a tachyonic Ricci-heating mechanism, significantly extending previous results in the literature. By performing 𝒪 (100) 3+1-dimensional classical lattice simulations, we explore the parameter space of two exemplary scenarios, numerically determining the main timescales in the process. Based on these results, we formulate a set of parametric equations that offer a practical approach for determining the efficiency of the heating process, the temperature at the onset of radiation domination, and the minimum number of e-folds of inflation needed to resolve the flatness and horizon problems in specific quintessential inflation scenarios. These parametric equations eliminate the need for additional lattice simulations, providing a convenient and efficient method for evaluating these key quantities.

Superconductors with a Topological Gap

I review a new superconductivity mechanism in which the gap is opened through a topological mechanism and not through the Landau mechanism of spontaneous symmetry breaking. As a consequence, the low-energy effective theory which describes these new superconductors is not the Landau–Ginzburg theory, formulated in terms of a local-order parameter, but a topological-field theory formulated in terms of emerging gauge fields. This new mechanism is realized as global superconductivty in Josephson junction arrays and in thin superconducting films with thicknesses comparable to the superconducting coherence length, which exhibits emergent granularity.

Cooperative quantum information erasure

We demonstrate an information erasure protocol that resets N qubits at once. The method displays exceptional performances in terms of energy cost (it operates nearly at Landauer energy cost kTln⁡2), time duration (∼μs) and erasure success rate (∼99,9%). The method departs from the standard algorithmic cooling paradigm by exploiting cooperative effects associated to the mechanism of spontaneous symmetry breaking which are amplified by quantum tunnelling phenomena. Such cooperative quantum erasure protocol is experimentally demonstrated on a commercial quantum annealer and could be readily applied in next generation hybrid gate-based/quantum-annealing quantum computers, for fast, effective, and energy efficient initialisation of quantum processing units.

Supersymmetry in the Geometric Representation of the Early Universe Wave Function

An approach to the geometric description of the birth and evolution of the universe is proposed. The wave function as the fundamental field is represented by a Clifford number with the transfer rules that possess the structure of the Dirac equation for any manifold. In terms of this geometric representation of the universe wave function, the nature of super-symmetry is explained. A probable mechanism of spontaneous symmetry breaking of the universe excitations with Bose and Fermi degrees of freedom is proposed.

Ultrafast imaging of spontaneous symmetry breaking in a photoionized molecular system

The Jahn-Teller effect is an essential mechanism of spontaneous symmetry breaking in molecular and solid state systems, and has far-reaching consequences in many fields. Up to now, to directly image the onset of Jahn-Teller symmetry breaking remains unreached. Here we employ ultrafast ion-coincidence Coulomb explosion imaging with sub-10 fs resolution and unambiguously image the ultrafast dynamics of Jahn-Teller deformations of {{rm{CH}}}_{4}^{+} cation in symmetry space. It is unraveled that the Jahn-Teller deformation from C3v to C2v geometries takes a characteristic time of 20 ± 7 fs for this system. Classical and quantum molecular dynamics simulations agree well with the measurement, and reveal dynamics for the build-up of the C2v structure involving complex revival process of multiple vibrational pathways of the {{rm{CH}}}_{4}^{+} cation.

Chiral Induction in Buckminsterfullerene Using a Metal–Organic Framework

AbstractChiral induction is an emerging topic of interest in various areas of chemistry because of its relationship to the elusive mechanism of spontaneous symmetry breaking in nature. Buckminsterfullerene (C60) with the shape of a highly symmetric truncated icosahedron has rarely been referred for chiral induction due to the difficult symmetry breaking. In this work, we demonstrate that a chiral metal–organic framework (MOF) can provide a key field for chiral induction. C60 could be incorporated into the chiral nanochannels of the MOF using an in situ self‐assembly strategy. The circular dichroism spectra of the resulting nanocomposites showed an intense chiral signal in the absorption region of C60. Experimental and theoretical studies showed that this unprecedented chiral induction of C60 was attributed to hybridization of the molecular orbitals through a close association with the pore surface of the MOF. Our method can endow highly symmetric achiral compounds with chirality, paving the new way toward fabrication of novel chiral nanomaterials.

Vanishing‐Harmonicity and Phase‐Change Materials

Phase‐change material (PCMs) store data using the contrast (electrical or optical) between two phases: a conductive crystalline phase and a weakly conductive amorphous phase. Most PCMs have a distorted octahedral structure. The contrast comes mainly from the electronic structure. In PCMs, a spontaneous symmetry breaking mechanism, the Peierls distortion, transforms the metallic crystalline structure into a lower‐density semiconducting structure. In a simple tight‐binding model of the covalent bond, the parameters that control this distortion, characterized by a parameter η, are analyzed. The effective interatomic potential E(η) is developed in a Landau‐type series in η: E(η) = E0 + E2η2 + E4η4. The PCMs with the largest contrast are those for which the effective potential E(η) of the crystalline phase has a disappearing harmonic contribution () and a vanishing electronic gap. This is called as an “incipient Peierls distortion.” It coincides with the so‐called “incipient metal”. The hardness of the repulsive potential and the number of electrons per atom play an important role. The vibrational properties and the anomalous Grüneisen parameter, specific to PCMs, are also studied.

Topological structures, spontaneous symmetry breaking and energy spectra in dipole hexagonal lattices

The interplay between the special triangular/hexagonal two dimensional lattice and the long range dipole–dipole interaction gives rise to topological defects, specifically the vortex, formed by a particular arrangement of the interacting classic dipoles. The nature of such vortices has been traditionally explained on the basis of numerical evidence. Here we propose the emerging formation of vortices as the natural minimum energy configuration of interacting (in-plane) two-dimensional dipoles based on the mechanism of spontaneous symmetry breaking. As opposed to the quantal case, where spin textures such as skyrmions or bimerons occur due to non-linearities in their Hamiltonian, it is still possible to witness classic topological structures due only to the nature of the dipole–dipole force. We shall present other (new) topological structures for the in-plane honeycomb lattice, as well as for two-dimensional out-of-plane dipoles. These structures will prove to be essential in the minimum energy configurations for three-dimensional simple hexagonal and hexagonal-closed-packed structures, whose energies in the bulk are obtained for the first time.

Variational technique for gauge boson masses

In this work, a novel mechanism for spontaneous symmetry breaking is presented. This mechanism avoids quadratic divergencies and is thus capable of addressing the hierarchy problem in gauge theories. Using the scale-dependent effective action $\Gamma_{k}$ minimally coupled to a gravitational sector, variational parameter setting is applied. This provides a mass and vacuum expectation value as a function of the constants arising in the low scale expansion of Newtons' and cosmological couplings. A comparison with experimental data, such as the Higgs mass, allows putting restrictions on these constants. With this generic approach one can compare with explicit candidates for an effective field theory of gravity. As an example, we use the asymptotic safety scenario, where we find restrictions on the matter content of the theory.

LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory

We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (LieAlgebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15. Program summaryProgram Title: LieART 2.0CPC Library link to program files:http://dx.doi.org/10.17632/8vm7j67bwt.1Licensing provisions: GNU Lesser General Public LicenseProgramming language: MathematicaExternal routines/libraries: Wolfram Mathematica 8–12Nature of problem: The use of Lie algebras and their representations is widespread in physics, especially in particle physics. The description of nature in terms of gauge theories requires the assignment of fields to representations of compact Lie groups and their Lie algebras. Mass and interaction terms in the Lagrangian give rise to the need for computing tensor products of representations of Lie algebras. The mechanism of spontaneous symmetry breaking leads to the application of subalgebra decomposition. This computer code was designed for the purpose of Grand Unified Theory (GUT) model building, (where compact Lie groups beyond the U(1), SU(2) and SU(3) of the Standard Model of particle physics are needed), but it has found use in a variety of other applications. Tensor product decomposition and subalgebra decomposition have been implemented for all classical Lie groups SU(N), SO(N) and Sp(2N) and all the exceptional groups E6, E7, E8, F4 and G2. This includes both regular and irregular (special) subgroup decomposition of all Lie groups up through rank 15, and many more.Solution method: LieART generates the weight system of an irreducible representation (irrep) of a Lie algebra by exploiting the Weyl reflection groups, which is inherent in all simple Lie algebras. Tensor products are computed by the application of Klimyk’s formula, except for SU(N)’s, where the Young-tableaux algorithm is used. Subalgebra decomposition of SU(N)’s are performed by projection matrices, which are generated from an algorithm to determine maximal subalgebras as originally developed by Dynkin [1,2]. We generate projection matrices by the Dynkin procedure, i.e., removing dots from the Dynkin or extended Dynkin diagram, for regular subalgebras, and we implement explicit projection matrices for special subalgebras.Restrictions: Internally irreps are represented by their unique Dynkin label. LieART’s default behavior in TraditionalForm is to print the dimensional name, which is the labeling preferred by physicist. Most Lie algebras can have more than one irrep of the same dimension and different irreps with the same dimension are usually distinguished by one or more primes (e.g. 175 and 175′ of A4). To determine the need for one or more primes of an irrep a brute-force loop over other irreps must be performed to search for irreps with the same dimensionality. Since Lie algebras have an infinite number of irreps, this loop must be cut off, which is done by limiting the maximum Dynkin digit in the loop. In rare cases for irreps of high dimensionality in high-rank algebras the used cutoff is too low and the assignment of primes is incorrect. However, this only affects the display of the irrep. All computations involving this irrep are correct, since the internal unique representation of Dynkin labels is used.

Statistical field theory and effective action method for scalar active matter

We employ Statistical Field Theory techniques for coarse-graining the steady-state properties of Active Ornstein-Uhlenbeck particles. The computation is carried on in the framework of the Unified Colored Noise approximation that allows an effective equilibrium picture. We thus develop a mean-field theory that allows to describe in a unified framework the phenomenology of scalar Active Matter. In particular, we are able to describe through spontaneous symmetry breaking mechanism two peculiar features of Active Systems that are (i) The accumulation of active particles at the boundaries of a confining container, and (ii) Motility-Induced Phase Separation (MIPS). \textcolor{black}{We develop a mean-field theory for steric interacting active particles undergoing to MIPS and for Active Lennard-Jones (ALJ) fluids.} \textcolor{black}{Within this framework}, we discuss the universality class of MIPS and ALJ \textcolor{black}{showing that it falls into Ising universality class.} We \textcolor{black}{thus} compute analytically the critical line $T_c(\tau)$ for both models. In the case of MIPS, $T_c(\tau)$ gives rise to a reentrant phase diagram compatible with an inverse transition from liquid to gas as the strength of the noise decreases. \textcolor{black}{However, in the case of particles interacting through anisotropic potentials, } the field theory acquires a $\varphi^3$ term that, \textcolor{black}{in general, cannot be canceled performing the expansion around the critical point.} In this case, the \textcolor{black}{Ising} critical point might \textcolor{black}{be replaced} by a first-order phase transition \textcolor{black}{region}.

A new mechanism for symmetry breaking from nilmanifolds

We present a method to obtain a scalar potential at tree level from a pure gauge theory on nilmanifolds, a class of negatively-curved compact spaces, and discuss the spontaneous symmetry breaking mechanism induced in the residual Minkowski space after compactification at low energy. We show that the scalar potential is completely determined by the gauge symmetries and the geometry of the compact manifold. In order to allow for simple analytic calculations we consider three extra space dimensions as the minimal example of a nilmanifold, therefore considering a pure Yang-Mills theory in seven dimensions.

Unique electronic structure of Tri-μ-oxido-[bis(porphyrinato)niobium(V)]: Spontaneous symmetry breaking mechanism of the special coordination skeleton

We report here the spontaneous symmetry breaking mechanism within the special tri-μ-oxido-[bis(porphyrinato)niobium(V)] (Nb2O3Por2) coordination skeleton. The driving force of the skeletal side-inclination is unveiled on the basis of DFT calculation results. In addition, a computational investigation for the purpose of predicting the reaction activity has also been carried out, revealing that its electrophilic reaction activity is directly related to the spontaneous symmetry breaking. Furthermore, the spontaneous symmetry breaking also destroys the electronic structural symmetry, rendering Nb2O3Por2 skeleton a novel bidirectional current ON-OFF switch controlled by the lights with different wavelengths.

Accelerating the Bone Healing Process by the Intervention of the Platelet Growth Factors Impregnated in Collagen. An experimental and theoretical mathematical model

A bone defect with standard dimensions and localization is produced. Inside this defect a polymer (collagen sponge) impregnated with growing factors, i. e. bone morphogenetic protein - BMP, is introduced. For the witness lot, the same defect is produced, in which the same polymer is introduced, but without any growing factors. It is found that the growing factor not only remains at the initial site, but also has effect on the bone regeneration process. A mathematical model is constructed using a field theory of multifractal type based on the spontaneous symmetry breaking mechanism to exploit such dynamics in biostructures. This mechanism contains all the informational �ingredients�: the multivalent logic based multifractal bit, the algorithm based networks through spatial cnoidal modes of oscilation, etc. In such context, the evolution of all biostructures, through a mechanism that mimics a 3D biological printer, can become operational.

The Deep Problems of Symmetry in Mathematical Physics and their Definitive Resolution

Symmetry stands for a central notion in Mathematics with extremely important applications in Theoretical Physics. Mathematician Emmy Noether in 1915 famously axiomatized this notion which resoundingly made its way in fundamental physics in its chapters of Lagrangian mechanics and Hamiltonian mechanics. However there is only one dimension to symmetry in mathematics and mathematical physics: an invariance that is preserved under a particular transformation. Contrary to this approach, there exist many other dimensions to the artifact of symmetry, which, if correctly prospected, could have helped accurately answer the long-running question in mathematical physics concerning the very origin of physical symmetries and the reason for the physical mechanism of spontaneous symmetry-breaking. The ignorance of origin of observable symmetries as well as the existence of other categories of symmetry is accompanied by a misunderstanding of the very states of symmetry, which is reflected in an inexact assessment of the ultra-structures subtending mathematical symmetry. In this writing, we aim to to expose the caveats of symmetry in mathematics, specifically in Geometry, as viewed from the overarching Quanto-Geometric perspective, and to show their resolution with the application of special Differential Geometry principles emanating from the Quanto-Geometric framework.

Two-dimensional Peierls instability via zone-boundary Dirac line nodes in layered perovskite oxides

Interplay of Fermi surface topology and electron correlation is the quintessential ingredient underlying spontaneous symmetry breaking in itinerant electronic systems. In one-dimensional (1D) systems at half-filling, the inherent Fermi surface nesting makes the translationally invariant metallic state unstable, which is known as Peierls instability. Extending the scope of Peierls instability to two (2D) or three dimensions (3D), however, is not straightforward, since the Fermi surface in higher dimensions is generally not nested. In this work, we show that a perfectly nested Fermi surface can be realized in a class of 2D perovskite oxides, giving rise to 2D Peierls instability. Here the central role is played by the zone boundary Dirac line node (DLN) protected by two orthogonal glide mirrors induced by the rotation of oxygen octahedra. Especially, at a critical angle of the octahedron rotation, the zone-boundary DLN flattens, leading to logarithmically diverging susceptibility. We propose the 2D Peierls instability driven by dispersionless DLN as a principle mechanism for spontaneous symmetry breaking in various layered perovskite oxides including the antiferromagnetism of Sr$_2$IrO$_4$. As a clear signature of the 2D Peierls instability, we predict that the magnetic domain wall in Sr$_2$IrO$_4$ hosts localized soliton modes.

Mirror symmetry breaking in toy models of developed turbulence

Importance of symmetry considerations in high energy physics and statistical systems in critical region is discussed. As a concrete example, the field theoretic renormalization group technique is applied to a general A model of active vector admixture b. Parameter A represents a continuous real parameter that governs the interaction structure of the system. The model encompasses the physically most relevant magnetohydrodynamic scenario (A = 1), and the model of linearized Navier-Stokes equations (A = −1). The environment is assumed to be in a state of fully developed turbulence, i.e. Reynolds number takes an infinite value. Additionally, spatial parity breaking is incorporated via the continuous parameter ρ. Studied system exhibits instability with respect to it, and large-scale generation of non-zero mean value 〈b〉 is observed. This is then explained in terms of spontaneous symmetry breaking mechanism.

Spontaneously broken symmetry restoration of quantum fields in the vicinity of neutral and electrically charged black holes

We consider the restoration of a spontaneously broken symmetry of an interacting quantum scalar field around neutral, i.e., Schwarzschild, and electrically charged, i.e., Reissner-Nordström, black holes in four dimensions. This is done through a semi-classical self-consistent procedure, by solving the system of non-linear coupled equations describing the dynamics of the background field and the vacuum polarization. The black hole at its own horizon generates an indefinitely high temperature which decreases to the Hawking temperature at infinity. Due to the high temperature in its vicinity, there forms a bubble around the black hole in which the scalar field can only assume a value equal to zero, a minimum of energy. Thus, in this region the symmetry of the energy and the field is preserved. At the bubble radius, there is a phase transition in the value of the scalar field due to a spontaneous symmetry breaking mechanism. Indeed, outside the bubble radius the temperature is low enough such that the scalar field settles with a nonzero value in a new energy minimum, indicating a breaking of the symmetry in this outer region. Conversely, there is symmetry restoration from the outer region to the inner bubble close to the horizon. Specific properties that emerge from different black hole electric charges are also noteworthy. It is found that colder black holes, i.e., more charged ones, have a smaller bubble length of restored symmetry. In the extremal case the bubble has zero length, i.e., there is no bubble. Additionally, for colder black holes, it becomes harder to excite the quantum field modes, so the vacuum polarization has smaller values. In the extremal case, the black hole temperature is zero and the vacuum polarization is never excited.

Aurora A depletion reveals centrosome-independent polarization mechanism in Caenorhabditis elegans.

How living systems break symmetry in an organized manner is a fundamental question in biology. In wild-type Caenorhabditis elegans zygotes, symmetry breaking during anterior-posterior axis specification is guided by centrosomes, resulting in anterior-directed cortical flows and a single posterior PAR-2 domain. We uncover that C. elegans zygotes depleted of the Aurora A kinase AIR-1 or lacking centrosomes entirely usually establish two posterior PAR-2 domains, one at each pole. We demonstrate that AIR-1 prevents symmetry breaking early in the cell cycle, whereas centrosomal AIR-1 instructs polarity initiation thereafter. Using triangular microfabricated chambers, we establish that bipolarity of air-1(RNAi) embryos occurs effectively in a cell-shape and curvature-dependent manner. Furthermore, we develop an integrated physical description of symmetry breaking, wherein local PAR-2-dependent weakening of the actin cortex, together with mutual inhibition of anterior and posterior PAR proteins, provides a mechanism for spontaneous symmetry breaking without centrosomes.