Mechanism Of Spontaneous Symmetry Breaking Research Articles

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.

Symmetry breaking in milling dynamics

Abstract Regenerative chatter vibrations arising during machining operations are a severe problem affecting the manufacturing production of high-precision mechanical components. A relatively deep understanding of this phenomenon when the cutting tool has equally spaced cutting teeth without runout has been achieved by now. However, real cutting tools are always affected by teeth runout in practical applications. Moreoever, they can be characterized by irregular geometries designed on purpose for enhancing their cutting performance. The most advanced dynamic milling models compute the effective tool-workpiece engagement conditions by taking into account the exact tool geometry and the nominal milling trochoidal kinematics. Nevertheless, they exclude the forced vibrations of the machining system from the stability analysis. In this work a more complete milling model is introduced, which takes into account the influence of forced vibrations on the effective tool-workpiece engagement conditions. By doing so, milling dynamics are linearized around the true steady state solution and a more correct stability analysis is carried out. The dynamic coupling between tool-workpiece engagement conditions and the steady state vibrations may arise even for small tool asymmetries and it gives rise to a kind of spontaneous symmetry breaking mechanism. This yet unexplained physical mechanism may have an important impact on the stability diagrams, as it will be demonstrated theoretically and experimentally in this work.

Field-induced phase coexistence in an artificial spin ice

Artificial spin-ice systems are magnetic metamaterials consisting of nanomagnet arrays that can be designed to study exotic magnetic states not found in natural materials. Typically, these arrays are modelled as interacting binary macrospins that can only be in an up or down state and are described by the Ising model. These materials have demonstrated ordering transitions, but only via a spontaneous symmetry-breaking mechanism. We have designed and studied a quadrupole artificial spin-ice system consisting of interacting plaquettes of coupled single-domain nanomagnets that can be interpreted as a composite, ternary variable. After annealing this system in an external magnetic field, we observe both a ferroquadrupolar and an antiferroquadrupolar phase, with an apparent first-order phase boundary and a coexistence regime. The phase diagram of this material is reminiscent of a model used to describe phase coexistence in the superfluid transition of 4He with 3He impurities. These results illustrate how composite magnetic objects realize exotic statistical physics models beyond the Ising model. Artificial spin-ice materials are usually described by spins that are either up or down. Here, a new type of spin ice is fabricated where the spins can be in one of three states with different coexisting phases separated by a first-order transition.

Topological interface states due to spontaneous symmetry breaking in a chain of anharmonic oscillators

In this work, we propose a one-dimensional system of coupled anharmonic oscillators with nonlinear coupling and study a spontaneous formation of interface excitations in the linearized spectrum of such periodic array. We show that during its evolution such system can undergo a topological transition from the disordered and topologically trivial phase into the nontrivial one. The topological transition is accompanied by the formation of the interface state in the spectrum of linearized excitations of the equilibrium state. Employing the technique based on the calculation of mean chiral displacement we demonstrate that the in-gap interface state exhibits a topological nature and is analogous to that in the well-known Su-Schrieffer-Heeger model. Our results demonstrate the formation of topological interface state induced by spontaneous symmetry breaking mechanism and open novel possibilities for designing various nonlinear electronic, photonic and polaritonic systems with disorder-robust control of information flows.

A new twist on heterotic string compactifications

A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail compactifications on a circle, where we find all the maximal gauge symmetry groups and the points where they arise. We present figures of two-dimensional slices of the 17-dimensional moduli space of Wilson lines and circle radii, showing the rich pattern of points and curves of symmetry enhancement. We then study the target space realization of the duality symmetry. Although the global continuous duality symmetries of dimensionally reduced heterotic supergravity are completely broken by the structure constants of the maximally enhanced gauge groups, the low energy effective action can be written in a manifestly duality covariant form using heterotic double field theory. As a byproduct, we show that a unique deformation of the generalized diffeomorphisms accounts for both SO(32) and E8 × E8 heterotic effective field theories, which can thus be considered two different backgrounds of the same double field theory even before compactification. Finally we discuss the spontaneous gauge symmetry breaking and Higgs mechanism that occurs when slightly perturbing the background fields, both from the string and the field theory perspectives.

Topological interface states mediated by spontaneous symmetry breaking

We propose a one-dimensional nonlinear system of coupled anharmonic oscillators that dynamically undergoes a topological transition switching from the {disordered} and topologically trivial phase into the nontrivial one due to the spontaneous symmetry breaking. The topological transition is accompanied by the formation of the topological interface state in the spectrum of linearized excitations of the stationary phase. Our findings thus highlight the potential of the nonlinear systems for hosting the topological phases and uncover a fundamental link between the spontaneous symmetry breaking mechanism and topological edge states.

The dark side of flipped trinification

We propose a model which unifies the Left-Right symmetry with the SU(3)L gauge group, called flipped trinification, and based on the SU(3)C ⊗ SU(3)L ⊗ SU(3)R ⊗ U(1)X gauge group. The model inherits the interesting features of both symmetries while elegantly explaining the origin of the matter parity, WP = (−1)3(B−L)+2s, and dark matter stability. We develop the details of the spontaneous symmetry breaking mechanism in the model, determining the relevant mass eigenstates, and showing how neutrino masses are easily generated via the seesaw mechanism. Moreover, we introduce viable dark matter candidates, encompassing a fermion, scalar and possibly vector fields, leading to a potentially novel dark matter phenomenology.

Spontaneous Symmetry Breaking and Higgs Mode: Comparing Gross-Pitaevskii and Nonlinear Klein-Gordon Equations

We discuss the mechanism of spontaneous symmetry breaking and the elementary excitations for a weakly-interacting Bose gas at a finite temperature. We consider both the non-relativistic case, described by the Gross-Pitaevskii equation, and the relativistic one, described by the cubic nonlinear Klein-Gordon equation. We analyze similarities and differences in the two equations and, in particular, in the phase and amplitude modes (i.e., Goldstone and Higgs modes) of the bosonic matter field. We show that the coupling between phase and amplitude modes gives rise to a single gapless Bogoliubov spectrum in the non-relativistic case. Instead, in the relativistic case the spectrum has two branches: one is gapless and the other is gapped. In the non-relativistic limit we find that the relativistic spectrum reduces to the Bogoliubov one. Finally, as an application of the above analysis, we consider the Bose-Hubbard model close to the superfluid-Mott quantum phase transition and we investigate the elementary excitations of its effective action, which contains both non-relativistic and relativistic terms.

Gravitational waves from dark first order phase transitions and dark photons**Supported by the Shanghai Municipality (KBH1512299) and Fudan University (JJH1512105)

Cold Dark Matter particles may interact with ordinary particles through a dark photon, which acquires a mass thanks to a spontaneous symmetry breaking mechanism. We discuss a dark photon model in which the scalar singlet associated to the spontaneous symmetry breaking has an effective potential that induces a first order phase transition in the early Universe. Such a scenario provides a rich phenomenology for electron-positron colliders and gravitational waves interferometers, and may be tested in several different channels. The hidden first order phase transition implies the emission of gravitational waves signals, which may constrain the dark photon’s space of parameters. Compared limits from electron-positron colliders, astrophysics, cosmology and future gravitational waves interferometers such as eLISA, U-DECIGO and BBO are discussed. This highly motivates a cross-checking strategy of data arising from experiments dedicated to gravitational waves, meson factories, the International Linear Collider (ILC), the Circular Electron Positron Collider (CEPC) and other underground direct detection experiments of cold dark matter candidates.

Spontaneous breaking of non-relativistic scale symmetry

We analyze the mechanism of spontaneous symmetry breaking of scale invariance in Galilean invariant field theories. We show that the existence of a dynamic gapless dilaton mode depends on whether the U(1) particle number or the Galilean boost symmetry are spontaneously broken. When both scale and particle number symmetries are spontaneously broken there is one propagating gapless Nambu-Goldstone mode. Its dispersion relation is linear if the chemical potential is nonzero and quadratic otherwise. We discuss the reversibility of RG flows in such theories.

Spontaneous symmetry breaking in replica field theory

In this paper we discuss a disordered $d$-dimensional Euclidean $\lambda\varphi^{4}$ model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each replica partition function, using the saddle-point equations and imposing the replica symmetric ansatz, we show the presence of a spontaneous symmetry breaking mechanism in the disordered model. Moreover, the leading replica partition function must be described by a large-$N$ Euclidean replica field theory. We discuss finite temperature effects considering periodic boundary condition in Euclidean time and also using the Landau-Ginzburg approach. In the low temperature regime we prove the existence of $N$ instantons in the model.

Large Hierarchy from Non-Minimal Coupling

In this paper, a model is proposed to solve the gauge hierarchy problem. Beyond the standard model, we introduce an extra scalar field that non-minimally couples to gravity. The fundamental scale is set at weak scale and Planck scale emerges dynamically by a spontaneous symmetry breaking mechanism.

First- and second-order metal-insulator phase transitions and topological aspects of a Hubbard-Rashba system

This paper considers a model consisting of a kinetic term, Rashba spin-orbit coupling and short-range Coulomb interaction at zero-temperature. The Coulomb interaction is decoupled by a mean-field approximation in the spin channel using field theory methods. The results feature a first-order phase transition for any finite value of the chemical potential and quantum criticality for vanishing chemical potential. The Hall conductivity is also computed using Kubo formula in a mean-field effective Hamiltonian. In the limit of infinite mass the kinetic term vanishes and all the phase transitions are of second order, in this case spontaneous symmetry breaking mechanism adds a ferromagnetic metallic phase to the system and features a zero-temperature quantization of the Hall conductivity in the insulating one.

Thomas Walter Bannerman Kibble

Thomas Walter Bannerman Kibble

Radiative Screening of Fifth Forces.

We describe a symmetron model in which the screening of fifth forces arises at the one-loop level through the Coleman-Weinberg mechanism of spontaneous symmetry breaking. We show that such a theory can avoid current constraints on the existence of fifth forces but still has the potential to give rise to observable deviations from general relativity, which could be seen in cold atom experiments.

Molecular model for chirality phenomena.

Chirality is a hallmark feature for molecular recognition in biology and chemical physics. We present a three-dimensional continuum model for studying chirality phenomena in condensed phases using molecular simulations. Our model system is based upon a simple four-site molecule and incorporates non-trivial kinetic behavior, including the ability to switch chirality or racemize, as well as thermodynamics arising from an energetic preference for specific chiral interactions. In particular, we introduce a chiral renormalization parameter that can locally favor either homochiral or heterochiral configurations. Using this model, we explore a range of chirality-specific phenomena, including the kinetics of chiral inversion, the mechanism of spontaneous chiral symmetry breaking in the liquid, chirally driven liquid-liquid phase separation, and chiral crystal structures.

Oscillations via Spike-Timing Dependent Plasticity in a Feed-Forward Model.

Neuronal oscillatory activity has been reported in relation to a wide range of cognitive processes including the encoding of external stimuli, attention, and learning. Although the specific role of these oscillations has yet to be determined, it is clear that neuronal oscillations are abundant in the central nervous system. This raises the question of the origin of these oscillations: are the mechanisms for generating these oscillations genetically hard-wired or can they be acquired via a learning process? Here, we study the conditions under which oscillatory activity emerges through a process of spike timing dependent plasticity (STDP) in a feed-forward architecture. First, we analyze the effect of oscillations on STDP-driven synaptic dynamics of a single synapse, and study how the parameters that characterize the STDP rule and the oscillations affect the resultant synaptic weight. Next, we analyze STDP-driven synaptic dynamics of a pre-synaptic population of neurons onto a single post-synaptic cell. The pre-synaptic neural population is assumed to be oscillating at the same frequency, albeit with different phases, such that the net activity of the pre-synaptic population is constant in time. Thus, in the homogeneous case in which all synapses are equal, the post-synaptic neuron receives constant input and hence does not oscillate. To investigate the transition to oscillatory activity, we develop a mean-field Fokker-Planck approximation of the synaptic dynamics. We analyze the conditions causing the homogeneous solution to lose its stability. The findings show that oscillatory activity appears through a mechanism of spontaneous symmetry breaking. However, in the general case the homogeneous solution is unstable, and the synaptic dynamics does not converge to a different fixed point, but rather to a limit cycle. We show how the temporal structure of the STDP rule determines the stability of the homogeneous solution and the drift velocity of the limit cycle.